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Thec-2d-Index of Oriented Matroids

✍ Scribed by Louis J Billera; Richard Ehrenborg; Margaret Readdy

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 453 KB
Volume: 80
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2797

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✦ Synopsis

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 S n . Finally, we show that only two-thirds of the :(S)'s of the lattice of flats are needed for the c-2d-index computation.

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