## 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 S_{n}. 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 language | English |
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Pages (from-to) | 79-105 |

Number of pages | 27 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 80 |

Issue number | 1 |

DOIs | |

State | Published - 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