Laplacian Immanantal polynomials and the GTS poset on Trees

Mukesh Kumar Nagar; Sivaramakrishnan Sivasubramanian

doi:10.1016/j.laa.2018.09.020

Laplacian Immanantal polynomials and the GTS poset on Trees

Combinatorics 2019-12-10 v2

Authors: 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.

Keywords

laplacian matrix immanantal polynomials trees poset characteristic polynomial q-laplacian graph theory

Cite

@article{arxiv.1710.02416,
  title  = {Laplacian Immanantal polynomials and the GTS poset on Trees},
  author = {Mukesh Kumar Nagar and Sivaramakrishnan Sivasubramanian},
  journal= {arXiv preprint arXiv:1710.02416},
  year   = {2019}
}

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