10 papers
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…
Lagrangian Matroids associated with Maps on Orientable Surfaces
Richard F. Booth, Alexandre V. Borovik, Israel Gelfand
The aim of the paper is to clarify the nature of combinatorial structures associated with maps on closed compact surfaces. We prove that maps give rise to Lagrangian matroids repre…
Noncommutative algebras associated to complexes and graphs
Israel Gelfand, Sergei Gelfand, Vladimir Retakh
This is a first of our papers devoted to "noncommutative topology and graph theory". Its origin is the paper math.QA/0002238 by I. Gelfand, V. Retakh, and R.L. Wilson where a new c…