منابع مشابه
More on additive triples of bijections
We study additive properties of the set S of bijections (or permutations) {1, . . . , n} → G, thought of as a subset of Gn, where G is an arbitrary abelian group of order n. Our main result is an asymptotic for the number of solutions to π1 + π2 + π3 = f with π1, π2, π3 ∈ S, where f : {1, . . . , n} → G is an arbitary function satisfying ∑n i=1 f(i) = ∑ G. This extends recent work of Manners, M...
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A new systematic approach for the speciication of bijections between sets of combinatorial objects is presented. It is based on the notion of object grammars. Object grammmars are recursive descriptions of objects which generalize context free grammars. The study of a particular substitution in these object grammars connrms once more the key role of Dyck words in the domain of enumerative and b...
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André proved that the number of alternating permutations on {1, 2, ..., n} is equal to the Euler number En. A refinement of André’s result was given by Entringer, who proved that counting alternating permutations according to the first element gives rise to Seidel’s triangle (En,k) for computing the Euler numbers. In a series of papers, using generating function method and induction, Poupard ga...
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We present an extensive survey of bijective proofs of classical partitions identities. While most bijections are known, they are often presented in a different, sometimes unrecognizable way. Various extensions and generalizations are added in the form of exercises.
متن کاملRestricted Tilings and Bijections
A classic problem in elementary combinatorics asks in how many ways one can tile a 1×n chessboard using 1× 1 and 1× 2 squares. The number of such tilings is the nth Fibonacci number. In a 2010 paper, Grimaldi generalized this problem by allowing for 1× 1 tiles to have one of w types and 1× 2 tiles to have one of t types and found that the solutions, in w and t, satisfied many of the same proper...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1999
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00045-0