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math.CO2026
Weighted bond posets and a new chromatic symmetric function
Rafael S. González D'León, Michelle L. Wachs
The classical bond lattice of a graph was used in a formula of Whitney to compute the chromatic polynomial. In this paper, we use weighted versions of the bond lattice, to introduc…
math.CO2024
On an -ary generalization of the Lie representation and tree Specht modules
Tamar Friedmann, Phil Hanlon, Michelle L. Wachs
We continue our study, initiated in our prior work with Richard Stanley, of the representation of the symmetric group on the multilinear component of an -ary generalization of t…
math.CO2024
A new presentation for Specht modules with distinct parts
Tamar Friedmann, Phil Hanlon, Michelle L. Wachs
We obtain a new presentation for Specht modules whose conjugate shapes have strictly decreasing parts by introducing a linear operator on the space generated by column tabloids. Th…