Compositions constrained by graph Laplacian minors
Abstract
Motivated by examples of symmetrically constrained compositions, super convex partitions, and super convex compositions, we initiate the study of partitions and compositions constrained by graph Laplacian minors. We provide a complete description of the multivariate generating functions for such compositions in the case of trees. We answer a question due to Corteel, Savage, and Wilf regarding super convex compositions, which we describe as compositions constrained by Laplacian minors for cycles; we extend this solution to the study of compositions constrained by Laplacian minors of leafed cycles. Connections are established and conjectured between compositions constrained by Laplacian minors of leafed cycles of prime length and algebraic/combinatorial properties of reflexive simplices.
Cite
@article{arxiv.1202.2013,
title = {Compositions constrained by graph Laplacian minors},
author = {Benjamin Braun and Robert Davis and Ashley Harrison and Jessica McKim and Jenna Noll and Clifford Taylor},
journal= {arXiv preprint arXiv:1202.2013},
year = {2012}
}