Abstract | ||
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We obtain an explicit method to compute thecd-index of the lattice of regions of an oriented matroid from theab-index of the corresponding lattice of flats. Since thecd-index of the lattice of regions is a polynomial in the ring Z(c,2d), we call it thec-2d-index. As an application we obtain a zonotopal analogue of a conjecture of Stanley: among all zonotopes the cubical lattice has the smallestc-2d-index coefficient-wise. We give a new combinatorial description for thec-2d-index of the cubical lattice and thecd-index of the Boolean algebra in terms of all the permutations in the symmetric groupSn. Finally, we show that only two-thirds of theα(S)'sof the lattice of flats are needed for thec-2d-index computation. |
Year | DOI | Venue |
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1997 | 10.1006/jcta.1997.2797 | Journal of Combinatorial Theory, Series A |
Keywords | DocType | Volume |
oriented matroid,indexation,boolean algebra | Journal | 80 |
Issue | ISSN | Citations |
1 | 0097-3165 | 16 |
PageRank | References | Authors |
1.33 | 0 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Louis J. Billera | 1 | 279 | 57.41 |
Richard Ehrenborg | 2 | 233 | 48.40 |
Margaret Readdy | 3 | 95 | 16.72 |