Cayley compositions,partitions, polytopes,and geometric bijections |
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Authors: | Matjaž Konvalinka Igor Pak |
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Affiliation: | 1. Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia;2. Department of Mathematics, UCLA, Los Angeles, CA 90095, USA |
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Abstract: | 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]. |
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Keywords: | Cayley composition Integer partition Convex polytope Ehrhart polynomial Bijective proof |
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