  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.
