Open Problems in

Algebraic Combinatorics

OPAC 2022 Conference

The University of Minnesota’s Open Problems in Algebraic Combinatorics conference (which was originally planned for 2020 but was pushed back two years because of the COVID-19 pandemic) will take place in person May 16-20 of 2022.

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…


Banff, Louise, and class P quivers

Open problems about the relationship between various classes of quivers coming from the theory of cluster algebras.

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 anti-commuting) variables.

From Schensted to Pólya

Open problems about relating the Pólya-Redfield 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.

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.

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