57 citations · 275 across the 73 of their papers we have counts for
8 papers · 1 filter
Deformed graphical zonotopal algebras
Boris Shapiro, Ilya Smirnov, Arkady Vaintrob
We study certain filtered deformations of the external zonotopal algebra of a given graph parametrized by univariate polynomials. We establish some general properties of these alge…
On algebras and matroids associated to undirected graphs
Boris Shapiro, Arkady Vaintrob
In this short note we make a few remarks on a class of generalized incidence matrices whose matroids do not depend on the orientation of the underlying graph and natural commutativ…
"K-theoretic" analog of Postnikov-Shapiro algebra distinguishes graphs
G. Nenashev, B. Shapiro
In this paper we study a filtered "K-theoretical" analog of a graded algebra associated to any loopless graph G which was introduced in \cite{PS}. We show that two such filtered al…
Using homological duality in consecutive pattern avoidance
Anton Khoroshkin, Boris Shapiro
Using the approach suggested in [arXiv:1002.2761] we present below a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential ge…
Around matrix-tree theorem
Yurii Burman, Boris Shapiro
Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the m…
Periodic de Bruijn triangles: exact and asymptotic results
B. Shapiro, M. Shapiro, A. Vainshtein
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic for…