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math.CO2026
Kronecker coefficients via the Giambelli identity for Schur functions
John M. Campbell
One of the central open problems in both algebraic combinatorics and representation theory is to find a positive combinatorial rule for Kronecker coefficients . A n…
math.CO2025
Partition algebras as monoid algebras
John M. Campbell
Wilcox has considered a twisted semigroup algebra structure on the partition algebra , but it appears that there has not previously been any known basis that give…
math.CO2025
Semisimple algebras related to immaculate tableaux
John M. Campbell
Given a direct sum of full matrix algebras, if there is a combinatorial interpretation associated with both the dimension of and the dimensions of the irreducible -modul…
math.CO2024
A lift of chromatic symmetric functions to
John M. Campbell
If we consider previously introduced extensions of Stanley's chromatic symmetric function for a graph to elements in the algebra of qu…