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DCG
2000

Mutation Polynomials and Oriented Matroids

13 years 10 months ago
Mutation Polynomials and Oriented Matroids
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 rationalvectorspacesofpolynomialsaredetermined,andbasesforthe Z-modulesgenerated 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.
J. Lawrence
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2000
Where DCG
Authors J. Lawrence
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