4 papers · 1 filter
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…
Quadratic-linar algebras associated with factorizations of noncommutative polynomials and noncommutative differential polynomials
Israel Gelfand, Vladimir Retakh, Robert Lee Wilson
This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined…