Sequentially Congruent Partitions and Related Bijections
نویسندگان
چکیده
منابع مشابه
Three Bijections on Set Partitions
We study three similar bijections on set partitions. The first gives a bijective proof of the equivalence of two statistics with a q-Stirling distribution, Milne’s statistic and the intertwining number. The second proves the equivalence of a multivariate block size distribution to a covering statistic. The third demonstrates equivalence of the number of all set partitions up to a given size to ...
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We study three similar bijections on set partitions. The first is an involution defined by Kasraoui and Zeng which proves the symmetry of the distribution of crossings and nestings. We show that a stronger result can be deduced. The second gives a bijective proof of the equivalence of two statistics with a q-Stirling distribution. The third proves the equivalence of a multivariate block size di...
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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 [K...
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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 obtain several extensions. We then extend this bijection to an affine linear map between convex polyhedra to give and new proof of Braun’s conjecture. As an application, we give a slight improv...
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A (set) partition of [n] = {1, 2, . . . , n} is a collection of mutually disjoint nonempty subsets, called blocks, of [n] whose union is [n]. We will write a partition as a sequence of blocks (B1, B2, . . . , Bk) such that min(B1) < min(B2) < · · · < min(Bk). There are two natural representations of a partition. Let π = (B1, B2, . . . , Bk) be a partition of [n]. The partition diagram of π is t...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2019
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-019-00451-w