Séminaire Lotharingien de Combinatoire, B83a (2021), 10 pp.
Mukesh Kumar Nagar and Sivaramakrishnan Sivasubramanian
Generalized Matrix Polynomials of Tree Laplacians Indexed
by Symmetric Functions and the GTS Poset
Let T be a tree on n vertices with Laplacian matrix
and q-Laplacian LTq.
Let GTSn be the generalized tree shift poset on the set of unlabelled
trees on n vertices. Inequalities are known between coefficients of the
immanantal polynomial of LT and
LTq as one moves up the poset
Using the Frobenius characteristic, this can be thought as a result involving the
Schur symmetric function sλ. In this paper, we use an arbitrary
symmetric function to define a generalized matrix function of an n x n matrix.
When the symmetric function is the monomial and the forgotten symmetric function,
we generalize such inequalities among coefficients of the generalized matrix polynomial of
LTq as one moves up the
Received: December 6, 2019.
Revised;: April 30, 2021.
Accepted: May 6, 2021.
Final Version: May 9, 2021.
The following versions are available: