The c-2d-index of oriented matroids

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40 Scopus citations

Abstract

We obtain an explicit method to compute the cd-index of the lattice of regions of an oriented matroid from the ab-index of the corresponding lattice of flats. Since the cd-index of the lattice of regions is a polynomial in the ring ℤ <c, 2d>, we call it the c-2d-index. As an application we obtain a zonotopal analogue of a conjecture of Stanley: among all zonotopes the cubical lattice has the smallest c-2d-index coefficient-wise. We give a new combinatorial description for the c-2d-index of the cubical lattice and the cd-index of the Boolean algebra in terms of all the permutations in the symmetric group Sn. Finally, we show that only two-thirds of the α(S)'s of the lattice of flats are needed for the c-2d-index computation.

Original languageEnglish
Pages (from-to)79-105
Number of pages27
JournalJournal of Combinatorial Theory. Series A
Volume80
Issue number1
DOIs
StatePublished - Oct 1997

Bibliographical note

Funding Information:
The authors thank the Mathematical Sciences Research Institute in Berkeley where some of this work was completed. The first author was supported in part by NSF Grant DMS-9500581.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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