location:  Publications → journals → CJM
Abstract view

# Valuations for Matroid Polytope Subdivisions

Published:2010-07-29
Printed: Dec 2010
• Federico Ardila,
San Francisco State University, San Francisco, CA, USA
• Alex Fink,
University of California, Berkeley, Berkeley, CA, USA
• Felipe Rincón,
Universidad de Los Andes, Bogotá, Colombia
 Format: HTML LaTeX MathJax PDF

## Abstract

We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.
 MSC Classifications: 05B35 - Matroids, geometric lattices [See also 52B40, 90C27] 52B40 - Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx] 52B45 - Dissections and valuations (Hilbert's third problem, etc.) 52C22 - Tilings in $n$ dimensions [See also 05B45, 51M20]