Laplacian Immanantal polynomials and the GTS poset on Trees

Abstract

Let $T$ be a tree on $n$ vertices with Laplacian $L_T$ and let $GT{S}_n$ be the generalized tree shift poset on the set of unlabelled trees on $n$ vertices. Inequalities are known for coefficients of the characteristic polynomial of $L_T$ as we go up the poset $GT{S}_n$. In this work, we generalize these inequalities to the $q$-Laplacian $L_T^q$ of $T$ and to the coefficients of all immanantal polynomials.

References in corpus (1)

• Hermitian adjacency matrix of digraphs and mixed graphs

Cited by in corpus (3)

• Eigenvalue monotonicity of $q$-Laplacians of trees along a poset
• Inequalities among two rowed immanants of the $q$-Laplacian of Trees and Odd height peaks in generalized Dyck paths
• Generalized Matrix polynomials of Tree Laplacians indexed by Symmetric functions and the GTS poset