Generalized Matrix polynomials of Tree Laplacians indexed by Symmetric functions and the GTS poset

Mukesh Kumar Nagar, Sivaramakrishnan Sivasubramanian

Let $T$ be a tree on $n$ vertices with $q$-Laplacian $L_T^q$ and Laplacian matrix $L_T$. Let $GT{S}_n$ be the generalized tree shift poset on the set of unlabelled trees on $n$ verti…