Open Problems in
Algebraic Combinatorics
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…
The Dedekind-MacNeille completion of Type B Bruhat order
An open problem about characterizing the Dedekind-MacNeille completion of the Type B Bruhat order as a subset of alternating sign matrices.
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.
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.
Two q,t-symmetry problems in symmetric function theory
Open problems about combinatorial proofs of the symmetry of various two-parameter 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 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.
A localized version of Greene’s theorem
Open problems about a “localized” version of Greene’s theorem on longest increasing subsequences in permutations.
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Open Problems in Algebraic Combinatorics 