Mutation Polynomials and Oriented Matroids |
| |
Authors: | J. Lawrence |
| |
Affiliation: | (1) Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA lawrence@gmu.edu, US |
| |
Abstract: | Several polynomials are of use in various enumeration problems concerning objects in oriented matroids. Chief among these is the Radon catalog. We continue to study these, as well as the total polynomials of uniform oriented matroids, by considering the effect on them of mutations of the uniform oriented matroid. The notion of a ``mutation polynomial' is introduced to facilitate the study. The affine spans of the Radon catalogs and the total polynomials in the appropriate rational vector spaces of polynomials are determined, and bases for the Z -modules generated by the mutation polynomials are found. The Radon polynomials associated with alternating oriented matroids are described; it is conjectured that a certain extremal property, like that held by cyclic polytopes among simplicial polytopes, is possessed by them. Received November 20, 1998, and in revised form August 21, 1999. Online publication May 19, 2000. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|