Séminaire Lotharingien de Combinatoire, 93B.137 (2025), 12 pp.
Sarah Brauner, Sylvie Corteel, Zajj Daugherty and Anne Schilling
Crystal Skeletons and their Axioms
Abstract.
Crystal skeletons were introduced by Maas-Gariépy in 2023 by contracting quasi-crystal components in a crystal graph. On the representation
theoretic level, crystal skeletons model the expansion of Schur functions into Gessel's quasisymmetric functions. Motivated by questions of Schur
positivity, we give a new axiomatic approach to crystal skeletons in analogy to the local Stembridge axioms for crystals. In addition, we provide a
combinatorial description of crystal skeletons, and prove many new properties, including a conjecture by Maas-Gariépy that crystal skeletons
generalize dual equivalence graphs.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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