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math.CO2023
Complete flagged homogeneous polynomials
Henry Ehrhard
We introduce a new basis for the polynomial ring which lifts the complete homogeneous symmetric polynomials while retaining representation theoretic significance. Using a specializ…
math.CO2022
A Crystal Analysis of -Arrays
Henry Ehrhard
Gasharov introduced the combinatorial objects known as -arrays to prove -positivity for the chromatic symmetric functions of incomparability graphs of (3+1)-free posets. We d…
math.CO2020
Kohnert's rule for flagged Schur modules
Sam Armon, Sami Assaf, Grant Bowling +1
Flagged Schur modules generalize the irreducible representations of the general linear group under the action of the Borel subalgebra. Their characters include many important gener…