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Combinatory Analysis, Volumes I and II
 
Percy A. MacMahon
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-4704-7735-6
Product Code:  CHEL/137.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Add to cart
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Combinatory Analysis, Volumes I and II
Percy A. MacMahon
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-4704-7735-6
Product Code:  CHEL/137.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Add to cart
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 137; 1984; 660 pp
    MSC: Primary 05

    By “combinatory analysis”, the author understands the part of combinatorics now known as “algebraic combinatorics”. In this book, the classical results of the outstanding 19th century school of British mathematicians are presented with great clarity and completeness.

    From the Introduction (1915): “The object of this work is, in the main, to present to mathematicians an account of theorems in combinatory analysis which are of a perfectly general character, and to show the connection between them by as far as possible bringing them together as parts of a general doctrine. It may appeal also to others whose reading has not been very extensive. They may not improbably find here some new points of view and suggestions which may prompt them to original investigation in a fascinating subject ...

    “In the present volume there appears a certain amount of original matter which has not before been published. It involves the author's preliminary researches in combinatory theory which have been carried out during the last thirty years. For the most part it is original work which, however, owes much to valuable papers by Cayley, Sylvester, and Hammond.”
    Readership

    Graduate students and research mathematicians.
  • Table of Contents
     
     
    • Front Cover
    • COMBINATORY ANALYSIS VOLUME I
    • INTRODUCTION
    • TABLE OF CONTENTS
    • SECTION I SYMMETRIC FUNCTIONS
    • CHAPTER I ELEMENTARY THEORY
    • 1.
    • 2.
    • 3.
    • 4.
    • 5.
    • 6.
    • 7.
    • CHAPTER II CONNEXION WITH THE THEORY OF DISTRIBUTIONS
    • 8.
    • 9.
    • 10.
    • 11.
    • 12.
    • 13.
    • 14.
    • 15.
    • 16.
    • 17.
    • 18.
    • 19.
    • CHAPTER III THE DISTRIBUTION INTO PARCELS AND GROUPS IN GENERAL
    • 20.
    • 21.
    • 22.
    • 23.
    • CHAPTER IV THE OPERATORS OF THE THEORY OF DISTRIBUTIONS
    • 25.
    • 26.
    • 27.
    • 28.
    • 29.
    • 30.
    • 31.
    • CHAPTER V APPLICATIONS OF THE OPERATORS d AND D
    • 32.
    • 33.
    • 34.
    • 35.
    • 36.
    • 37.
    • 38.
    • 39.
    • SECTION II THEORY OF SEPARATIONS
    • CHAPTER I THE ALGEBRAIC THEORY
    • 40.
    • 41.
    • 42.
    • 43.
    • 44.
    • 45.
    • 46.
    • 47.
    • CHAPTER II GENERALIZATION OF WARING'S FORMULA
    • 48.
    • 49.
    • CHAPTER III THE DIFFERENTIAL OPERATORS OF THE THEORY OF SEPARATIONS
    • 50.
    • 51.
    • 52.
    • CHAPTER IV A CALCULUS OF BINOMIAL COEFFICIENTS
    • 53.
    • 54.
    • 55.
    • CHAPTER V THEORY OF THREE IDENTITIES
    • 56.
    • 57.
    • 58.
    • 59.
    • 60.
    • SECTION III PERMUTATIONS
    • CHAPTER I THE ENUMERATION OF PERMUTATIONS
    • 61.
    • 62.
    • CHAPTER II THE THEORY OF PERMUTATIONS
    • 63.
    • 64.
    • 65.
    • 66.
    • 67.
    • CHAPTER III THE THEORY OF DISPLACEMENTS
    • 68.
    • 69.
    • 70.
    • 71.
    • 72.
    • 73.
    • 74.
    • 75.
    • 76.
    • 77.
    • 78.
    • 79.
    • 80.
    • 81.
    • 82.
    • 83.
    • CHAPTER IV OTHER APPLICATIONS OF THE MASTER THEOREM
    • 84.
    • 85.
    • 86.
    • 87.
    • 88.
    • 89.
    • 90.
    • 91.
    • 92.
    • CHAPTER V LATTICE PERMUTATIONS
    • 93.
    • 94.
    • 95.
    • 96.
    • 97.
    • 98.
    • 99.
    • 100.
    • 101.
    • 102.
    • 103.
    • CHAPTER VI THE INDICES OF PERMUTATIONS
    • 104.
    • 105.
    • 106.
    • 107.
    • 108.
    • 109.
    • 110.
    • 111.
    • 112.
    • 113.
    • 114.
    • 115.
    • 116.
    • 117.
    • 118.
    • 119.
    • 120.
    • SECTION IV THEORY OF THE COMPOSITIONS OF NUMBERS
    • CHAPTER I UNIPARTITE NUMBERS
    • 121.
    • 122.
    • 123.
    • 124.
    • 125.
    • 126.
    • 127.
    • 128.
    • 129.
    • CHAPTER II MULTIPARTITE NUMBERS
    • 130.
    • 131.
    • 132.
    • 133.
    • 134.
    • 135.
    • 136.
    • 137.
    • 138.
    • 139.
    • 140.
    • 141.
    • 142.
    • 143.
    • 143.
    • 144.
    • 145.
    • 146.
    • 147.
    • 148.
    • CHAPTER III THE GRAPHICAL REPRESENTATION OF THE COMPOSITIONS OF TRIPARTITE AND MULTIPARTITE NUMBERS
    • 149.
    • 150.
    • 151.
    • 152.
    • 153.
    • 154.
    • 155.
    • CHAPTER IV SIMON NEWCOMB'S PROBLEM
    • 156.
    • 157.
    • 158.
    • 159.
    • 160.
    • 161.
    • 162.
    • 163.
    • 164.
    • 166.
    • CHAPTER V GENERALIZATION OF THE FOREGOING THEORY
    • 167.
    • 168.
    • 169.
    • 170.
    • 171.
    • 172.
    • 173.
    • 174.
    • 175.
    • 176.
    • 177.
    • 178.
    • 179.
    • 180.
    • 181.
    • 182.
    • SECTION V DISTRIBUTIONS UPON A CHESS BOARD, TO WHICH IS PREFIXED A CHAPTER ON PERFECT PARTITIONS
    • CHAPTER I THEORY OF PERFECT PARTITIONS OF NUMBERS
    • 183.
    • 184.
    • 185.
    • 186.
    • 187.
    • 188.
    • 189.
    • CHAPTER II ARRANGEMENTS ON A CHESS BOARD
    • 190.
    • 191.
    • 192.
    • 193.
    • 194.
    • 195.
    • 196.
    • 197.
    • 198.
    • 199.
    • 200.
    • 201.
    • 202.
    • 203.
    • 204.
    • 205.
    • 206.
    • CHAPTER III THE THEORY OF THE LATIN SQUARE
    • 207.
    • 208.
    • 209.
    • 210.
    • 211.
    • 212.
    • 213.
    • 214.
    • 215.
    • 216.
    • 217.
    • 218.
    • 219.
    • 220.
    • 221.
    • 222.
    • 223.
    • 224.
    • SECTION VI THE ENUMERATION OF THE PARTITIONS OF MULTIPARTITE NUMBERS
    • CHAPTER I ENUMERATION OF THE PARTITIONS OF BIPARTITE NUMBERS
    • 225.
    • 226.
    • 227.
    • 228.
    • 229.
    • 230.
    • CHAPTER II ENUMERATION OF THE PARTITIONS OF TRIPARTITE AND OTHER MULTIPARTITE NUMBERS
    • 231.
    • 232.
    • 233.
    • 234.
    • 235.
    • 236.
    • 237.
    • TABLES
    • COMBINATORY ANALYSIS VOLUME II
    • INTRODUCTION
    • NOTE ON WARING'S FORMULA FOR THE SUM OF THE POWERS OF THE ROOTS OF AN EQUATION
    • TABLE OF CONTENTS
    • SECTION VII THE PARTITION OF NUMBERS
    • CHAPTER I THE THEORY OF EULER
    • 238.
    • 239.
    • 240.
    • 241.
    • 242.
    • 243.
    • 244.
    • 245.
    • 246.
    • 247.
    • 248.
    • 249.
    • 250.
    • CHAPTER II GEOMETRICAL AND OTHER TRANSFORMATIONS
    • 251.
    • 252.
    • 253.
    • 254.
    • 255.
    • 256.
    • 257.
    • 258.
    • 259.
    • 260.
    • 261.
    • 262.
    • 263.
    • 264.
    • 265.
    • 266.
    • 267.
    • 268.
    • 269.
    • 270.
    • 271.
    • 272.
    • 273.
    • 274.
    • 275.
    • CHAPTER III RAMANUJAN'S IDENTITIES
    • 276.
    • 277.
    • 278.
    • 279.
    • 280.
    • 281.
    • 282.
    • 283.
    • 284.
    • 285.
    • 286.
    • 287.
    • 288.
    • 289.
    • 290.
    • 291.
    • 292.
    • 293.
    • 294.
    • 295.
    • 296.
    • CHAPTER IV PARTITIONS WITHOUT SEQUENCES
    • 297.
    • 298.
    • 299.
    • 300.
    • 301.
    • 302.
    • 303.
    • CHAPTER V PARTICULAR STUDY OF THE FUNCTION
    • 304.
    • 305.
    • 306.
    • 307.
    • 308.
    • 309.
    • 310.
    • 311.
    • 312.
    • 313.
    • 314.
    • 315.
    • 316.
    • 317.
    • 318.
    • 319.
    • 320.
    • 321.
    • 322.
    • 323.
    • 324.
    • 325.
    • 326.
    • 327.
    • 328.
    • 329.
    • 330.
    • 331.
    • 332.
    • 333.
    • CHAPTER VI CONNEXION OF THE THEORY OF PARTITIONS WITH OTHER COMBINATORY THEORIES
    • 334.
    • 335.
    • 336.
    • 337.
    • 338.
    • SECTION VIII A NEW BASIS OF THE THEORY OF PARTITIONS. PARTITION ANALYSIS IN SEVEN CHAPTERS
    • CHAPTER I THE METHOD OF DIOPHANTINE INEQUALITIES
    • 339.
    • 340.
    • 341.
    • 342.
    • 343.
    • 344.
    • 345.
    • 346.
    • 347.
    • 348.
    • 349.
    • 350.
    • 351.
    • 352.
    • 353.
    • 354.
    • CHAPTER II A SYZYGETIC THEORY
    • 355.
    • 356.
    • 357.
    • 358.
    • 359.
    • CHAPTER III THE DIOPHANTINE INEQUALITY
    • 360.
    • 361.
    • 362.
    • 363.
    • 364.
    • 365.
    • 366.
    • 367.
    • 368.
    • 369.
    • 370.
    • 371.
    • 372.
    • 373.
    • 374.
    • CHAPTER IV THE SIMULTANEOUS DIOPHANTINE INEQUALlTlES
    • 375.
    • 376.
    • 377.
    • 378.
    • 379.
    • 380.
    • 381.
    • CHAPTER V ON THE FORM OF ENUMERATING FUNCTIONS
    • 382.
    • 383.
    • 384.
    • 385.
    • 386.
    • 387.
    • 388.
    • 389.
    • 390.
    • 391.
    • 392.
    • 393.
    • 394.
    • 395.
    • 396.
    • 397.
    • 398.
    • CHAPTER VI ON THE ALGEBRAIC FORMS OF INTEGERS
    • 399.
    • 400.
    • 401.
    • 402.
    • 403.
    • CHAPTER VII THE THEORY OF MAGIC SQUARES
    • 404.
    • 405.
    • 406.
    • 407.
    • 408.
    • 409.
    • 410.
    • 411.
    • 412.
    • 413.
    • 414.
    • 415.
    • 416.
    • 417.
    • 418.
    • 419.
    • SECTION IX PARTITIONS IN TWO DIMENSIONS
    • CHAPTER I INTRODUCTORY NOTIONS
    • 420.
    • 421.
    • 422.
    • 423.
    • 424.
    • 425.
    • 426.
    • 427.
    • 428.
    • CHAPTER II THE METHOD OF DIOPHANTINE INEQUALITIES
    • 429.
    • 430.
    • 431.
    • 432.
    • 433.
    • 484.
    • 435.
    • CHAPTER III THE METHOD OF LATTICE FUNCTIONS
    • 436.
    • 437.
    • 438.
    • 439.
    • 440.
    • 441.
    • 442.
    • 443.
    • 444.
    • 445.
    • 446.
    • 447.
    • 448.
    • 449.
    • 450.
    • 451.
    • 452.
    • CHAPTER IV EXCURSUS ON PERMUTATION FUNCTIONS
    • 453.
    • 454.
    • 455.
    • 456.
    • 457.
    • 458.
    • 459.
    • 460.
    • 461.
    • 462.
    • 463.
    • SECTION X COMPLETION OF THE THEORY OF SECTION IX
    • CHAPTER I PLANE PARTITIONS WITH UNRESTRICTED PART MAGNITUDE
    • 464.
    • 465.
    • 466.
    • 467.
    • 468.
    • 469.
    • 470.
    • 471.
    • 472.
    • 473.
    • 474.
    • 475.
    • 476.
    • 477.
    • 478.
    • 479.
    • 480.
    • 481.
    • 482.
    • 483.
    • 484.
    • 485.
    • 486.
    • 487.
    • 488.
    • 489.
    • CHAPTER II PLANE PARTITIONS WITH RESTRICTED PART MAGNITUDE
    • 490.
    • 491.
    • 492.
    • 493.
    • 494.
    • 495.
    • 496.
    • 497.
    • 498.
    • CHAPTER III PARTITIONS IN SOLIDO
    • 499.
    • 500.
    • 501.
    • 502.
    • 503.
    • 504.
    • 505.
    • 506.
    • 507.
    • 508.
    • CHAPTER IV THE SYMMETRY APPERTAINING TO PARTITIONS
    • 509.
    • 510.
    • 511.
    • 512.
    • 513.
    • 514.
    • 515.
    • 516.
    • 517.
    • 518.
    • 519.
    • 520.
    • 521.
    • 522.
    • 523.
    • 524.
    • 525.
    • 526.
    • 527.
    • 528.
    • 529.
    • 530.
    • 531.
    • 532.
    • 533.
    • 534.
    • SECTION XI SYMMETRIC FUNCTIONS OF SEVERAL SYSTEMS OF QUANTITIES, WITH SOME APPLICATIONS TO DISTRIBUTION THEORY
    • CHAPTER I ELEMENTARY THEORY
    • 535.
    • 536.
    • 537.
    • 538.
    • CHAPTER II THE THEORY OF SEPARATIONS AND THE ALLIED THEORY OF DISTRIBUTIONS
    • 539.
    • 540.
    • 541.
    • 542.
    • 543.
    • 544.
    • 545.
    • 546.
    • CHAPTER III THE DIFFERENTIAL OPERATIONS
    • 547.
    • 548.
    • 549.
    • 550.
    • 551.
    • 552.
    • 553.
    • 554.
    • 555.
    • CHAPTER IV THE LINEAR PARTIAL DIFFERENTIAL OPERATORS OF THE THEORY OF SEPARATIONS AND THE PARTITION-OBLITERATING OPERATORS
    • 556.
    • 557.
    • 558.
    • 559.
    • 560.
    • 561.
    • 562.
    • 563.
    • 564.
    • 565.
    • 566.
    • 567.
    • 568.
    • CHAPTER V FURTHER THEORY OF THE LATIN SQUARE
    • 569.
    • 570.
    • 571.
    • TABLES OF SYMMETRIC FUNCTIONS OF TWO SYSTEMS OF QUANTITIES
    • INDEX TO THE TWO VOLUMES
    • Back Cover
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
AMS Chelsea Publishing
Volume: 137; 1984; 660 pp
MSC: Primary 05

By “combinatory analysis”, the author understands the part of combinatorics now known as “algebraic combinatorics”. In this book, the classical results of the outstanding 19th century school of British mathematicians are presented with great clarity and completeness.

From the Introduction (1915): “The object of this work is, in the main, to present to mathematicians an account of theorems in combinatory analysis which are of a perfectly general character, and to show the connection between them by as far as possible bringing them together as parts of a general doctrine. It may appeal also to others whose reading has not been very extensive. They may not improbably find here some new points of view and suggestions which may prompt them to original investigation in a fascinating subject ...

“In the present volume there appears a certain amount of original matter which has not before been published. It involves the author's preliminary researches in combinatory theory which have been carried out during the last thirty years. For the most part it is original work which, however, owes much to valuable papers by Cayley, Sylvester, and Hammond.”
Readership

Graduate students and research mathematicians.
  • Front Cover
  • COMBINATORY ANALYSIS VOLUME I
  • INTRODUCTION
  • TABLE OF CONTENTS
  • SECTION I SYMMETRIC FUNCTIONS
  • CHAPTER I ELEMENTARY THEORY
  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • CHAPTER II CONNEXION WITH THE THEORY OF DISTRIBUTIONS
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • CHAPTER III THE DISTRIBUTION INTO PARCELS AND GROUPS IN GENERAL
  • 20.
  • 21.
  • 22.
  • 23.
  • CHAPTER IV THE OPERATORS OF THE THEORY OF DISTRIBUTIONS
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
  • CHAPTER V APPLICATIONS OF THE OPERATORS d AND D
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • SECTION II THEORY OF SEPARATIONS
  • CHAPTER I THE ALGEBRAIC THEORY
  • 40.
  • 41.
  • 42.
  • 43.
  • 44.
  • 45.
  • 46.
  • 47.
  • CHAPTER II GENERALIZATION OF WARING'S FORMULA
  • 48.
  • 49.
  • CHAPTER III THE DIFFERENTIAL OPERATORS OF THE THEORY OF SEPARATIONS
  • 50.
  • 51.
  • 52.
  • CHAPTER IV A CALCULUS OF BINOMIAL COEFFICIENTS
  • 53.
  • 54.
  • 55.
  • CHAPTER V THEORY OF THREE IDENTITIES
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • SECTION III PERMUTATIONS
  • CHAPTER I THE ENUMERATION OF PERMUTATIONS
  • 61.
  • 62.
  • CHAPTER II THE THEORY OF PERMUTATIONS
  • 63.
  • 64.
  • 65.
  • 66.
  • 67.
  • CHAPTER III THE THEORY OF DISPLACEMENTS
  • 68.
  • 69.
  • 70.
  • 71.
  • 72.
  • 73.
  • 74.
  • 75.
  • 76.
  • 77.
  • 78.
  • 79.
  • 80.
  • 81.
  • 82.
  • 83.
  • CHAPTER IV OTHER APPLICATIONS OF THE MASTER THEOREM
  • 84.
  • 85.
  • 86.
  • 87.
  • 88.
  • 89.
  • 90.
  • 91.
  • 92.
  • CHAPTER V LATTICE PERMUTATIONS
  • 93.
  • 94.
  • 95.
  • 96.
  • 97.
  • 98.
  • 99.
  • 100.
  • 101.
  • 102.
  • 103.
  • CHAPTER VI THE INDICES OF PERMUTATIONS
  • 104.
  • 105.
  • 106.
  • 107.
  • 108.
  • 109.
  • 110.
  • 111.
  • 112.
  • 113.
  • 114.
  • 115.
  • 116.
  • 117.
  • 118.
  • 119.
  • 120.
  • SECTION IV THEORY OF THE COMPOSITIONS OF NUMBERS
  • CHAPTER I UNIPARTITE NUMBERS
  • 121.
  • 122.
  • 123.
  • 124.
  • 125.
  • 126.
  • 127.
  • 128.
  • 129.
  • CHAPTER II MULTIPARTITE NUMBERS
  • 130.
  • 131.
  • 132.
  • 133.
  • 134.
  • 135.
  • 136.
  • 137.
  • 138.
  • 139.
  • 140.
  • 141.
  • 142.
  • 143.
  • 143.
  • 144.
  • 145.
  • 146.
  • 147.
  • 148.
  • CHAPTER III THE GRAPHICAL REPRESENTATION OF THE COMPOSITIONS OF TRIPARTITE AND MULTIPARTITE NUMBERS
  • 149.
  • 150.
  • 151.
  • 152.
  • 153.
  • 154.
  • 155.
  • CHAPTER IV SIMON NEWCOMB'S PROBLEM
  • 156.
  • 157.
  • 158.
  • 159.
  • 160.
  • 161.
  • 162.
  • 163.
  • 164.
  • 166.
  • CHAPTER V GENERALIZATION OF THE FOREGOING THEORY
  • 167.
  • 168.
  • 169.
  • 170.
  • 171.
  • 172.
  • 173.
  • 174.
  • 175.
  • 176.
  • 177.
  • 178.
  • 179.
  • 180.
  • 181.
  • 182.
  • SECTION V DISTRIBUTIONS UPON A CHESS BOARD, TO WHICH IS PREFIXED A CHAPTER ON PERFECT PARTITIONS
  • CHAPTER I THEORY OF PERFECT PARTITIONS OF NUMBERS
  • 183.
  • 184.
  • 185.
  • 186.
  • 187.
  • 188.
  • 189.
  • CHAPTER II ARRANGEMENTS ON A CHESS BOARD
  • 190.
  • 191.
  • 192.
  • 193.
  • 194.
  • 195.
  • 196.
  • 197.
  • 198.
  • 199.
  • 200.
  • 201.
  • 202.
  • 203.
  • 204.
  • 205.
  • 206.
  • CHAPTER III THE THEORY OF THE LATIN SQUARE
  • 207.
  • 208.
  • 209.
  • 210.
  • 211.
  • 212.
  • 213.
  • 214.
  • 215.
  • 216.
  • 217.
  • 218.
  • 219.
  • 220.
  • 221.
  • 222.
  • 223.
  • 224.
  • SECTION VI THE ENUMERATION OF THE PARTITIONS OF MULTIPARTITE NUMBERS
  • CHAPTER I ENUMERATION OF THE PARTITIONS OF BIPARTITE NUMBERS
  • 225.
  • 226.
  • 227.
  • 228.
  • 229.
  • 230.
  • CHAPTER II ENUMERATION OF THE PARTITIONS OF TRIPARTITE AND OTHER MULTIPARTITE NUMBERS
  • 231.
  • 232.
  • 233.
  • 234.
  • 235.
  • 236.
  • 237.
  • TABLES
  • COMBINATORY ANALYSIS VOLUME II
  • INTRODUCTION
  • NOTE ON WARING'S FORMULA FOR THE SUM OF THE POWERS OF THE ROOTS OF AN EQUATION
  • TABLE OF CONTENTS
  • SECTION VII THE PARTITION OF NUMBERS
  • CHAPTER I THE THEORY OF EULER
  • 238.
  • 239.
  • 240.
  • 241.
  • 242.
  • 243.
  • 244.
  • 245.
  • 246.
  • 247.
  • 248.
  • 249.
  • 250.
  • CHAPTER II GEOMETRICAL AND OTHER TRANSFORMATIONS
  • 251.
  • 252.
  • 253.
  • 254.
  • 255.
  • 256.
  • 257.
  • 258.
  • 259.
  • 260.
  • 261.
  • 262.
  • 263.
  • 264.
  • 265.
  • 266.
  • 267.
  • 268.
  • 269.
  • 270.
  • 271.
  • 272.
  • 273.
  • 274.
  • 275.
  • CHAPTER III RAMANUJAN'S IDENTITIES
  • 276.
  • 277.
  • 278.
  • 279.
  • 280.
  • 281.
  • 282.
  • 283.
  • 284.
  • 285.
  • 286.
  • 287.
  • 288.
  • 289.
  • 290.
  • 291.
  • 292.
  • 293.
  • 294.
  • 295.
  • 296.
  • CHAPTER IV PARTITIONS WITHOUT SEQUENCES
  • 297.
  • 298.
  • 299.
  • 300.
  • 301.
  • 302.
  • 303.
  • CHAPTER V PARTICULAR STUDY OF THE FUNCTION
  • 304.
  • 305.
  • 306.
  • 307.
  • 308.
  • 309.
  • 310.
  • 311.
  • 312.
  • 313.
  • 314.
  • 315.
  • 316.
  • 317.
  • 318.
  • 319.
  • 320.
  • 321.
  • 322.
  • 323.
  • 324.
  • 325.
  • 326.
  • 327.
  • 328.
  • 329.
  • 330.
  • 331.
  • 332.
  • 333.
  • CHAPTER VI CONNEXION OF THE THEORY OF PARTITIONS WITH OTHER COMBINATORY THEORIES
  • 334.
  • 335.
  • 336.
  • 337.
  • 338.
  • SECTION VIII A NEW BASIS OF THE THEORY OF PARTITIONS. PARTITION ANALYSIS IN SEVEN CHAPTERS
  • CHAPTER I THE METHOD OF DIOPHANTINE INEQUALITIES
  • 339.
  • 340.
  • 341.
  • 342.
  • 343.
  • 344.
  • 345.
  • 346.
  • 347.
  • 348.
  • 349.
  • 350.
  • 351.
  • 352.
  • 353.
  • 354.
  • CHAPTER II A SYZYGETIC THEORY
  • 355.
  • 356.
  • 357.
  • 358.
  • 359.
  • CHAPTER III THE DIOPHANTINE INEQUALITY
  • 360.
  • 361.
  • 362.
  • 363.
  • 364.
  • 365.
  • 366.
  • 367.
  • 368.
  • 369.
  • 370.
  • 371.
  • 372.
  • 373.
  • 374.
  • CHAPTER IV THE SIMULTANEOUS DIOPHANTINE INEQUALlTlES
  • 375.
  • 376.
  • 377.
  • 378.
  • 379.
  • 380.
  • 381.
  • CHAPTER V ON THE FORM OF ENUMERATING FUNCTIONS
  • 382.
  • 383.
  • 384.
  • 385.
  • 386.
  • 387.
  • 388.
  • 389.
  • 390.
  • 391.
  • 392.
  • 393.
  • 394.
  • 395.
  • 396.
  • 397.
  • 398.
  • CHAPTER VI ON THE ALGEBRAIC FORMS OF INTEGERS
  • 399.
  • 400.
  • 401.
  • 402.
  • 403.
  • CHAPTER VII THE THEORY OF MAGIC SQUARES
  • 404.
  • 405.
  • 406.
  • 407.
  • 408.
  • 409.
  • 410.
  • 411.
  • 412.
  • 413.
  • 414.
  • 415.
  • 416.
  • 417.
  • 418.
  • 419.
  • SECTION IX PARTITIONS IN TWO DIMENSIONS
  • CHAPTER I INTRODUCTORY NOTIONS
  • 420.
  • 421.
  • 422.
  • 423.
  • 424.
  • 425.
  • 426.
  • 427.
  • 428.
  • CHAPTER II THE METHOD OF DIOPHANTINE INEQUALITIES
  • 429.
  • 430.
  • 431.
  • 432.
  • 433.
  • 484.
  • 435.
  • CHAPTER III THE METHOD OF LATTICE FUNCTIONS
  • 436.
  • 437.
  • 438.
  • 439.
  • 440.
  • 441.
  • 442.
  • 443.
  • 444.
  • 445.
  • 446.
  • 447.
  • 448.
  • 449.
  • 450.
  • 451.
  • 452.
  • CHAPTER IV EXCURSUS ON PERMUTATION FUNCTIONS
  • 453.
  • 454.
  • 455.
  • 456.
  • 457.
  • 458.
  • 459.
  • 460.
  • 461.
  • 462.
  • 463.
  • SECTION X COMPLETION OF THE THEORY OF SECTION IX
  • CHAPTER I PLANE PARTITIONS WITH UNRESTRICTED PART MAGNITUDE
  • 464.
  • 465.
  • 466.
  • 467.
  • 468.
  • 469.
  • 470.
  • 471.
  • 472.
  • 473.
  • 474.
  • 475.
  • 476.
  • 477.
  • 478.
  • 479.
  • 480.
  • 481.
  • 482.
  • 483.
  • 484.
  • 485.
  • 486.
  • 487.
  • 488.
  • 489.
  • CHAPTER II PLANE PARTITIONS WITH RESTRICTED PART MAGNITUDE
  • 490.
  • 491.
  • 492.
  • 493.
  • 494.
  • 495.
  • 496.
  • 497.
  • 498.
  • CHAPTER III PARTITIONS IN SOLIDO
  • 499.
  • 500.
  • 501.
  • 502.
  • 503.
  • 504.
  • 505.
  • 506.
  • 507.
  • 508.
  • CHAPTER IV THE SYMMETRY APPERTAINING TO PARTITIONS
  • 509.
  • 510.
  • 511.
  • 512.
  • 513.
  • 514.
  • 515.
  • 516.
  • 517.
  • 518.
  • 519.
  • 520.
  • 521.
  • 522.
  • 523.
  • 524.
  • 525.
  • 526.
  • 527.
  • 528.
  • 529.
  • 530.
  • 531.
  • 532.
  • 533.
  • 534.
  • SECTION XI SYMMETRIC FUNCTIONS OF SEVERAL SYSTEMS OF QUANTITIES, WITH SOME APPLICATIONS TO DISTRIBUTION THEORY
  • CHAPTER I ELEMENTARY THEORY
  • 535.
  • 536.
  • 537.
  • 538.
  • CHAPTER II THE THEORY OF SEPARATIONS AND THE ALLIED THEORY OF DISTRIBUTIONS
  • 539.
  • 540.
  • 541.
  • 542.
  • 543.
  • 544.
  • 545.
  • 546.
  • CHAPTER III THE DIFFERENTIAL OPERATIONS
  • 547.
  • 548.
  • 549.
  • 550.
  • 551.
  • 552.
  • 553.
  • 554.
  • 555.
  • CHAPTER IV THE LINEAR PARTIAL DIFFERENTIAL OPERATORS OF THE THEORY OF SEPARATIONS AND THE PARTITION-OBLITERATING OPERATORS
  • 556.
  • 557.
  • 558.
  • 559.
  • 560.
  • 561.
  • 562.
  • 563.
  • 564.
  • 565.
  • 566.
  • 567.
  • 568.
  • CHAPTER V FURTHER THEORY OF THE LATIN SQUARE
  • 569.
  • 570.
  • 571.
  • TABLES OF SYMMETRIC FUNCTIONS OF TWO SYSTEMS OF QUANTITIES
  • INDEX TO THE TWO VOLUMES
  • Back Cover
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