A Bijection between Necklaces and Multisets with Divisible Subset Sum
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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In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force approach of verifying all combinations of integers, several solutions have been found, ranging from clever uses of various data structures to computationally...
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Recall from Garsia’s paper that Ba is the group algebra Q(Sn) element Ba = 1 2 3 · · · a Wa,n = ∑ α∈Sa α Wa,n, where Wa,n is the word Wa,n = (a+ 1)(a+ 2) · · ·n. The motivation is that we have a deck of cards labelled 1, 2, . . . , n, and Ba represents all possible decks that may result from removing the cards 1, 2, . . . , a and then inserting them back into the deck (consisting of the cards a...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/7804