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Transplanting Trees: Chromatic Symmetric Function Results through the Group Algebra of
Angèle M. Foley, Joshua Kazdan, Larissa Kröll +3
One of the major outstanding conjectures in the study of chromatic symmetric functions (CSF's) states that trees are uniquely determined by their CSF's. Though verified on graphs o…
H-chromatic symmetric functions
Nancy Mae Eagles, Angèle M. Foley, Alice Huang +2
We introduce -chromatic symmetric functions, , which use the -coloring of a graph to define a generalization of Stanley's chromatic symmetric functions. We say…
Factorial supersymmetric skew Schur functions and ninth variation determinantal identities
Angèle M. Foley, Ronald C. King
The determinantal identities of Hamel and Goulden have recently been shown to apply to a tableau-based ninth variation of skew Schur functions. Here we extend this approach and its…
Determinantal and Pfaffian identities for ninth variation skew Schur functions and Q-functions
Angèle M. Foley, Ronald C. King
Recently Okada defined algebraically ninth variation skew Q-functions, in parallel to Macdonald's ninth variation skew Schur functions. Here we introduce a skew shifted tableaux de…
Spiders and their Kin: An Investigation of Stanley's Chromatic Symmetric Function for Spiders and Related Graphs
Angèle M. Foley, Joshua Kazdan, Larissa Kröll +3
We study the chromatic symmetric functions of graph classes related to spiders, namely generalized spider graphs (line graphs of spiders), and what we call horseshoe crab graphs. W…
Classes of graphs with e-positive chromatic symmetric function
Angèle M. Foley, Chính T. Hoàng, Owen D. Merkel
In the mid-1990s, Stanley and Stembridge conjectured that the chromatic symmetric functions of claw-free co-comparability (also called incomparability) graphs were e-positive. The…
Resolving Stanley's -positivity of claw-contractible-free graphs
Samantha Dahlberg, Angele Foley, Stephanie van Willigenburg
In Stanley's seminal 1995 paper on the chromatic symmetric function, he stated that there was no known graph that was not contractible to the claw and whose chromatic symmetric fun…