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math.CO2026
Matching algebras and their Dunkl subalgebras
Darij Grinberg, Anatol Kirillov, Boris Shapiro
For a finite simple graph , we consider the quotient algebra of the polynomial ring in the variables (for ) by the ideal generated by all…
math.CO2026
The Loopy Polynomial: from Tutte's Universal -Function to Bizonotopal Geometry
Anatol Kirillov, Gleb Nenashev, Boris Shapiro +1
We study the loopy polynomial L_G, a multivariate graph invariant arising from bizonotopal graph algebras and defined by a deletion-loopy-contraction recursion, in which the contra…
math.PR2026
Structured perturbations of tridiagonal twisted Toeplitz matrices
Dario Giandinoto, Boris Shapiro
Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values…