Open Problems in
Algebraic Combinatorics

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OPAC Conference Postponed Again
Because of the ongoing nature of the COVID19 pandemic, the University of Minnesota’s Open Problems in Algebraic Combinatorics conference, which was scheduled for May 18–22, 2020, and was tentatively rescheduled for 2021, has been postponed again. The likely date of the conference will now be May 1620 of 2022, two years from the original date.… Read more

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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…

Banff, Louise, and class P quivers
Open problems about the relationship between various classes of quivers coming from the theory of cluster algebras.

OPAC 2022 Proceedings Articles
The OPAC 2022 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.

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. UPDATE : The conference has… Read more

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.