Open Problems in
Algebraic Combinatorics

Featured
OPAC Conference Postponed
Because of the COVID19 pandemic, the University of Minnesota’s Open Problems in Algebraic Combinatorics conference, which was scheduled for May 18–22, 2020, has been postponed. The likely date of the conference will be May 1721 of 2021, a year from the original date. See the conference website for more information.

Featured
Welcome to the OPAC blog!
The OPAC blog is for members of algebraic combinatorics community to share open problems with each other. To submit an entry, please…

OPAC 2021 Proceedings Articles
The OPAC 2021 conference will be accompanied by a proceedings to be published by the AMS, and some of the articles for the proceedings are now available on the conference website. These articles also discuss open problems in algebraic combinatorics, in somewhat more detail than the posts featured on this blog.

Isomorphisms of zonotopal algebras
An open problem about the classification up to isomorphism of certain algebras associated to graphs (and zonotopes).

Coinvariants and harmonics
An open problem about understanding the coinvariants of the symmetric group action on polynomials in multiple sets of (commuting and anticommuting) variables.

Two q,tsymmetry problems in symmetric function theory
Open problems about combinatorial proofs of the symmetry of various twoparameter polynomials coming from algebra.

On the multiplication table of Jack polynomials
Open problems about positivity properties of the structure constants associated to Jack polynomials.

From Schensted to Pólya
Open problems about relating the PólyaRedfield theory and tableaux combinatorics.

Descent sets for tensor powers
An open problem about understanding combinatorially the characters of the symmetric group acting on tensor powers of representations of a reductive group.

A localized version of Greene’s theorem
Open problems about a “localized” version of Greene’s theorem on longest increasing subsequences in permutations.

The restriction problem
An open problem about the restriction of irreducible general linear group representations to the subgroup of permutation matrices.