Overview

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.

Full Product Details

Author:   Christine Berkesch ,  Benjamin Brubaker ,  Gregg Musiker ,  Pavlo Pylyavskyy
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   110
ISBN:  

9781470473334

ISBN 10:   147047333
Pages:   371
Publication Date:   31 October 2024
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Articles Francois 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 Feray, 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

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Author Information

Christine Berkesch, University of Minnesota, Twin Cities, Minneapolis, MN, Benjamin Brubaker, University of Minnesota, Twin Cities, Minneapolis, MN, Gregg Musiker, University of Minnesota, Twin Cities, Minneapolis, MN, Pavlo Pylyavskyy, University of Minnesota, Twin Cities, Minneapolis, MN, and Victor Reiner, University of Minnesota, Twin Cities, Minneapolis, MN.

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