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Thec-2d-Index of Oriented Matroids

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Publication Date
Volume
80
Issue
1
Identifiers
DOI: 10.1006/jcta.1997.2797
Disciplines
  • Mathematics

Abstract

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, 2 d), we call it the c-2 d-index. As an application we obtain a zonotopal analogue of a conjecture of Stanley: among all zonotopes the cubical lattice has the smallest c-2 d-index coefficient-wise. We give a new combinatorial description for the c-2 d-index of the cubical lattice and the cd-index of the Boolean algebra in terms of all the permutations in the symmetric group S n . Finally, we show that only two-thirds of the α( S)' sof the lattice of flats are needed for the c-2 d-index computation.

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