93 citations · 107 across the 8 of their papers we have counts for
10 papers
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…
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…
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…
Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov +1
We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart po…
Bizonotopal Graphical Algebras
Anatol Kirillov, Gleb Nenashev, Boris Shapiro +1
Zonotopal algebras (external, central, and internal) of an undirected graph G introduced by Postnikov-Shapiro and Holtz-Ron, are finite-dimensional commutative graded algebras whos…
Semiclassical expansion for exactly solvable differential operators
Jorge A. Borrego-Morell, Boris Shapiro
Below we study a linear differential equation $\MM (v(z,η))=η^M{v(z,η)}$, where is a large spectral parameter and $\MM=\sum_{k=1}^{M}ρ_{k}(z)\frac{d^k}{dz^k},\; M\ge 2$ is a…