Contents I. Introduction 1 II. Definitions and Preliminaries 4 2.1 Definitions and Notation 4 2.2 Two involutions and nonintersecting lattice paths . . . . 7 III. Counting by Major Index 13 3.1 Without restrictions 13 3.2 With a diagonal boundary 16 3.3 Tableaux generating functions 26 IV. Counting by Strange Major Index 33 4.1 Without restrictions 34 4.2 With a diagonal boundary 37 4.3 Tableaux generating functions 50 V . Detailed Proofs and Auxiliary Results 58 5.1 The major index and strange major index generating functions for lattice paths without restrictions 58 5.2 A correspondence for lattice paths that cross the line x y 62 5.3 A correspondence for pairs of intersecting lattice paths 73 5.4 Correspondences between tableaux and nonintersecting lattice paths 87 5.5 A determinant lemma 99 5.6 A multiple basic hypergeometric summation 101 References 108
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