A bijection between words and multisets of necklaces
نویسندگان
چکیده
منابع مشابه
A bijection between words and multisets of necklaces
In [4] has been proved the bijectivity of a natural mapping Φ from words on a totally ordered alphabet onto multisets of primitive necklaces (circular words) on this alphabet. This mapping has many enumerative applications; among them, the fact that the number of permutations in a given conjugation class and with a given descent set is equal to the scalar product of two representations naturall...
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We give a bijective proof of a conjecture of Regev and Vershik [7] on the equality of two multisets of hook numbers of certain skew-Young diagrams. The bijection proves a result that is stronger and more symmetric than the original conjecture, by means of a construction involving Dyck paths, a particular type of lattice path.
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We construct a bijection proving that the following two sets have the same cardinality: (i) the set of words over {−1, 0, 1} of length m−2 which have every initial sum nonnegative, and (ii) the set of partitions of {1, 2, . . . ,m} such that no two consecutive numbers lie in the same block and for no four numbers the middle two are in one block and the end two are in another block. The words we...
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چکیده ندارد.
Eulerian digraphs and Dyck words, a bijection
The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions. The connection between Dyck words and Eulerian digraphs exploits a novel combinatorial structure: a binary matrix, we call Dyck matrix, representing the cycles of an Eulerian digraph. 1. Background, and ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2012.03.016