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….

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.

On the cohomology of the Grassmannian
A conjecture about the Hilbert series for the subalgebra of the cohomology ring of the Grassmannian generated by elements of degree at most some fixed number.

Sorting via chipfiring
Conjectures about various “labeled” versions of chipfiring on the integer lattice.

The rank and cranks
Problems and conjectures on statistics related to the Ramanujan congruences for integer partitions.