A. Kirillov

The Loopy Polynomial: from Tutte's Universal $V$-Function to Bizonotopal Geometry

We study the loopy polynomial L_G, a multivariate graph invariant arising from bizonotopal graphical algebras and defined by deletion and loopy contraction, in which the contracted edge is retained as a loop. It determines the Tutte polynomial and admits a spanning-forest expansion recording external activity component...