Cayley compositions, partitions, polytopes, and geometric bijections

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:123

Article

Konvalinka, Matjaz¹  Pak, Igor² 

[1] Univ Ljubljana, Dept Math, Ljubljana, Slovenia

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

关键词: Cayley composition;    Integer partition;    Convex polytope;    Ehrhart polynomial;    Bijective proof;   

DOI  :  10.1016/j.jcta.2013.11.008

来源: Elsevier

【 摘 要 】

In 1857, Cayley showed that certain sequences, now called Cayley compositions, are equinumerous with certain partitions into powers of 2. In this paper we give a simple bijective proof of this result and a geometric generalization to equality of Ehrhart polynomials between two convex polytopes. We then apply our results to give a new proof of Braun's conjecture proved recently by the authors [15]. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free