منابع مشابه
On Stanley’s Reciprocity Theorem for Rational Cones
We give a short, self-contained proof of Stanley’s reciprocity theorem for a rational cone K ⊂ R. Namely, let σK(x) = ∑ m∈K∩Zd x m. Then σK(x) and σK◦(x) are rational functions which satisfy the identity σK(1/x) = (−1) σK◦(x). A corollary of Stanley’s theorem is the Ehrhart-Macdonald reciprocity theorem for the lattice-point enumerator of rational polytopes. A distinguishing feature of our proo...
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Normaliz is a program for the computation of Hilbert bases of rational cones and the normalizations of affine monoids. It may also be used for solving diophantine linear systems. In this paper we present the algorithms implemented in the program.
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Acknowledgements First of all I would like to thank my advisor Winfried Bruns for his inspiring guidance and support. Our discussions have been very helpful, and I am always enjoying to work with him. I also wish to thank all my colleagues at the Institute for Mathematics. They are providing a very pleasant working atmosphere. Many thanks also to Merle for listening to my incomprehensible disco...
متن کاملThe poset of bipartitions
Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on bipartitional relations given by inclusion. We show that, with respect to this partial order, the bipartitional relations on a set of size [Formula: see text] for...
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It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen–Macaulay order complex in exactly the same conditions. The group theoretical tools used are relatively elementary, and avoid the classification of finite simple groups and of minimal finite simple groups. © 2006 Elsevi...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2018
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2018.292.103