163 citations · 287 across the 18 of their papers we have counts for
18 papers
Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs
Israel Gelfand, Sergei Gelfand, Vladimir Retakh +1
To directed graphs with unique sink and source we associate a noncommutative associative alsgebra and a polynomial over this algebra. Edges of the graph correspond to pseudo-roots…
On a class of algebras associated to directed graphs
Israel Gelfand, Vladimir Retakh, Shirlei Serconek +1
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Suc…
Quaternionic quasideterminants and determinants
Israel Gelfand, Vladimir Retakh, Robert Lee Wilson
We compute quaisideterminants and determinants of quaternionic matrices
Hilbert series of quadratic algebras associated with pseudo-roots of noncommutative polynomials
Israel Gelfand, Sergei Gelfand, Vladimir Retakh +2
The quadratic algebras Q_n are associated with pseudo-roots of noncommutative polynomials. We compute the Hilbert series of the algebras Q_n and of the dual quadratic algebras Q_n^…
Fundamental Solutions for the Tricomi Operator, II
J. Barros-Neto, Israel M. Gelfand
We explicitly calculate fundamental solutions for the Tricomi operator relative to a point in the hyperbolic region and show that these solutions originate from the hypergeometric…
Oriented Lagrangian Matroids
Richard F. Booth, Alexandre V. Borovik, Israel M. Gelfand +1
In this paper we present a definition of oriented Lagrangian symplectic matroids and their representations. Classical concepts of orientation and this extension may both be thought…