20 citations · 35 across the 15 of their papers we have counts for
18 papers
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 graphical algebras and defined by deletion and loopy contraction, in which the contracted…
Hypercube subgroups of (outer) reduced Weyl groups of the Cuntz algebras
Francesco Brenti, Roberto Conti, Gleb Nenashev
We develop some tools, of an algebraic and combinatorial nature, which enable us to obtain a detailed description of certain quadratic subgroups of the (outer) reduced Weyl group o…
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…
Repeatable patterns and the maximum multiplicity of a generator in a reduced word
Christian Gaetz, Yibo Gao, Pakawut Jiradilok +2
We study the maximum multiplicity of a simple transposition in a reduced word for the longest permutation , a…
Differential operators on Schur and Schubert polynomials
Gleb Nenashev
This paper deals with decreasing operators on back stable Schubert polynomials. We study two operators and of degree , which satisfy the Leibniz rule. Furthermore,…
Classification of external Zonotopal algebras
Gleb Nenashev
In this paper we work with power algebras associated to hyperplane arrangements. There are three main types of these algebras, namely, external, central, and internal zonotopal alg…
On ideals generated by two generic quadratic forms in the exterior algebra
Veronica Crispin Quiñonez, Samuel Lundqvist, Gleb Nenashev
Based on the structure theory of pairs of skew-symmetric matrices, we give a conjecture for the Hilbert series of the exterior algebra modulo the ideal generated by two generic qua…
Trianguloids and Triangulations of Root Polytopes
Pavel Galashin, Gleb Nenashev, Alexander Postnikov
Triangulations of a product of two simplices and, more generally, of root polytopes are closely related to Gelfand-Kapranov-Zelevinsky's theory of discriminants, to tropical geomet…
On -deformations of Postnikov-Shapiro algebras
Anatol N. Kirillov, Gleb Nenashev
For any given loopless graph , we introduce - deformations of its Postnikov-Shapiro algebras counting spanning trees, counting spanning forests and - deformations of int…
Secant degeneracy index of the standard strata in the space of binary forms
Gleb Nenashev, Boris Shapiro, Michael Shapiro
The space $Pol_d\simeq \bC P^d$ of all complex-valued binary forms of degree (considered up to a constant factor) has a standard stratification, each stratum of which contains…
"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…
A note on Fröberg's conjecture for forms of equal degrees
Gleb Nenashev
In this note by using elementary considerations, we settle Fröberg's conjecture for a large number of cases, when all generators of ideals have the same degree.
Postnikov-Shapiro Algebras, Graphical Matroids and their generalizations
Gleb Nenashev
In this paper we consider the original and different generalizations of Postnikov-Shapiro algebra which enumerate forests and trees of graphs, see~\cite{PSh}. Our main result is th…
On commutative algebra associated to -labeled subforests of a graph
Gleb Nenashev
For a given graph , we construct an associated commutative algebra, whose dimension is equal to the number of -labeled forests of . We show that the dimension of the -t…
Counting the minimal number of inflections of a plane curve
Gleb Nenashev
Given a plane curve , we consider the problem of determining the minimal number of inflections which curves $\mbox{diff}(γ)$ may have, where $\mbox{di…
A short proof of Kotzig's theorem
Gleb Nenashev
A new shortest proof of Kotzig's Theorem about graphs with unique perfect matching is presented in this paper. It is well known that Kotzig's theorem is a consequence of Yeo's Theo…
On existence of noncritical vertices in digraphs
G. V. Nenashev
Let be a strongly connected digraphs on vertices. A vertex of is noncritical, if the digraph is strongly connected. We prove, that if sum of the degrees…
An Upper bound on the chromatic number of circle graphs without
G. V. Nenashev
Let be a circle graph without clique on 4 vertices. We prove that the chromatic number of doesn't exceed 30.