Open Problems in
Algebraic Combinatorics

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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…

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OPAC Conference 2020
The University of Minnesota will be hosting a conference May 18–22, celebrating Open Problems in Algebraic Combinatorics….

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.

Root polytope projections
Open problems about projections of root polytopes onto subspaces.

Descents and cyclic descents
Open problems about descents of permutations and tableaux, and their cyclic analogues.

Matrix counting over finite fields
Conjectures about the polynomials which count matrices over finite fields with prescribed rank and location of nonzero entries.

The Schur cone and the cone of log concavity
Conjectures and problems about understanding the cone generated by products of Schur functions corresponding to partitions with bounded length.