图Laplacian子式约束下的合成
Compositions constrained by graph Laplacian minors
摘要：
受对称约束的组合物，超凸分区，超凸组合物的例子的启发，我们开始研究的分区和组合物的限制图拉普拉斯未成年人。我们提供了一个完整的描述的多元生成函数的情况下，这样的组合物的树。我们回答了一个问题，由于科蒂尔，萨维奇和Wilf关于超凸的组成，我们描述为组成的拉普拉斯未成年人的周期约束，我们扩展这个解决方案的研究组成的拉普拉斯未成年人的叶周期约束。连接的建立和approximately由拉普拉斯未成年人的素数长度和代数/组合性质的自反单形的叶圈约束的成分之间。
英文摘要：
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.
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