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| Softcover ISBN: | 978-1-4704-7333-4 |
| Product Code: | PSPUM/110 |
| List Price: | $139.00 |
| MAA Member Price: | $125.10 |
| AMS Member Price: | $111.20 |
| eBook ISBN: | 978-1-4704-7797-4 |
| Product Code: | PSPUM/110.E |
| List Price: | $137.00 |
| MAA Member Price: | $123.30 |
| AMS Member Price: | $109.60 |
| Softcover ISBN: | 978-1-4704-7333-4 |
| eBook ISBN: | 978-1-4704-7797-4 |
| Product Code: | PSPUM/110.B |
| List Price: | $276.00 $207.50 |
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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 110; 2024; 371 ppMSC: Primary 05; 13; 52; 82; 14
In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume.
The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
ReadershipGraduate students and research mathematicians interested in algebraic combinatorics and related areas.
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Table of Contents
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Articles
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François Bergeron — $(\operatorname {GL}_k \times \ \mathbb {S}_n)$-modules of multivariate diagonal harmonics
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Francesco Brenti — Some open problems on Coxeter groups and unimodality
-
R. Kenyon — Some combinatorial problems arising in the dimer model
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Per Alexandersson and Valentin Féray — A positivity conjecture on the structure constants of shifted Jack functions
-
Greta Panova — Complexity and asymptotics of structure constants
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Jonathan Novak and Brendon Rhoades — Increasing subsequences and Kronecker coefficients
-
Nathan Williams — Combinatorics and braid varieties
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Isabella Novik and Hailun Zheng — Neighborly spheres and transversal numbers
-
Hugh Thomas — Realizing simplicial complexes as the boundary of the totally non-negative part of a variety
-
Sam Hopkins — Order polynomial product formulas and poset dynamics
-
Thomas Lam — An invitation to positive geometries
-
Satoshi Murai — An upper bound problem for triangulations of manifolds
-
Igor Pak — What is a combinatorial interpretation?
-
James Propp — Trimer covers in the triangular grid: Twenty mostly open problems
-
Laura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling and Mike Zabrocki — The mystery of plethysm coefficients
-
Tri Lai — Problems in the enumeration of tilings
-
Zhao Gao, Claudiu Raicu and Keller VandeBogert — Some questions arising from the study of cohomology on flag varieties
-
Alexander Yong — Castelnuovo-Mumford regularity and Schubert geometry
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Ralf Schiffler — Perfect matching problems in cluster algebras and number theory
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-
Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume.
The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
Graduate students and research mathematicians interested in algebraic combinatorics and related areas.
-
Articles
-
François Bergeron — $(\operatorname {GL}_k \times \ \mathbb {S}_n)$-modules of multivariate diagonal harmonics
-
Francesco Brenti — Some open problems on Coxeter groups and unimodality
-
R. Kenyon — Some combinatorial problems arising in the dimer model
-
Per Alexandersson and Valentin Féray — A positivity conjecture on the structure constants of shifted Jack functions
-
Greta Panova — Complexity and asymptotics of structure constants
-
Jonathan Novak and Brendon Rhoades — Increasing subsequences and Kronecker coefficients
-
Nathan Williams — Combinatorics and braid varieties
-
Isabella Novik and Hailun Zheng — Neighborly spheres and transversal numbers
-
Hugh Thomas — Realizing simplicial complexes as the boundary of the totally non-negative part of a variety
-
Sam Hopkins — Order polynomial product formulas and poset dynamics
-
Thomas Lam — An invitation to positive geometries
-
Satoshi Murai — An upper bound problem for triangulations of manifolds
-
Igor Pak — What is a combinatorial interpretation?
-
James Propp — Trimer covers in the triangular grid: Twenty mostly open problems
-
Laura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling and Mike Zabrocki — The mystery of plethysm coefficients
-
Tri Lai — Problems in the enumeration of tilings
-
Zhao Gao, Claudiu Raicu and Keller VandeBogert — Some questions arising from the study of cohomology on flag varieties
-
Alexander Yong — Castelnuovo-Mumford regularity and Schubert geometry
-
Ralf Schiffler — Perfect matching problems in cluster algebras and number theory
