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arXiv · 1710.02416

Laplacian Immanantal polynomials and the GTS poset on Trees

Mukesh Kumar Nagar·Sivaramakrishnan Sivasubramanian
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Abstract

Let $T$ be a tree on $n$ vertices with Laplacian $L_T$ and let $GTS_n$ 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 $GTS_n$. In this work, we generalize these inequalities to the $q$-Laplacian $L^q_T$ of $T$ and to the coefficients of all immanantal polynomials.

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Mukesh Kumar Nagar, Sivaramakrishnan Sivasubramanian. 2018-02-27. Laplacian Immanantal polynomials and the GTS poset on Trees. https://doi.org/10.1016/j.laa.2018.09.020

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