Constructed Tableaux and a new Shifted Littlewood--Richardson Rule
We develop a new combinatorial rule to compute the coefficients of the projective representation theory of symmetric groups and cohomology of orthogonal Grassmannians. It is exponentially faster than Stembridge's rule in some families of structure coefficients. Our analysis also yields the first algebraic proof of Serrano's Littlewood-Richardson rule.
Jan 1, 2025
A universal characterization of the shifted plactic monoid
The shifted plactic monoid is a generalization of the plactic monoid based on Haiman's mixed insertion. We show that its discovery is inevitable in the sense that it is universal among all monoids respecting the plactic relations, and whose reading words are hook words.
Jan 1, 2024
Generalized lattice-point visibility in $Bbb N^k$
Jan 1, 2021