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Softcover ISBN:  9781470473334 
Product Code:  PSPUM/110 
List Price:  $139.00 
MAA Member Price:  $125.10 
AMS Member Price:  $111.20 
eBook ISBN:  9781470477974 
Product Code:  PSPUM/110.E 
List Price:  $137.00 
MAA Member Price:  $123.30 
AMS Member Price:  $109.60 
Softcover ISBN:  9781470473334 
eBook ISBN:  9781470477974 
Product Code:  PSPUM/110.B 
List Price:  $276.00 $207.50 
MAA Member Price:  $248.40 $186.75 
AMS Member Price:  $220.80 $166.00 

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.

Table of Contents

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 nonnegative 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 — CastelnuovoMumford regularity and Schubert geometry

Ralf Schiffler — Perfect matching problems in cluster algebras and number theory


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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 nonnegative 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 — CastelnuovoMumford regularity and Schubert geometry

Ralf Schiffler — Perfect matching problems in cluster algebras and number theory