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An almost‐bijective proof of an asymptotic property of partitions
Author(s) -
Jaggard Aaron D.
Publication year - 2007
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20180
Subject(s) - bijection , mathematics , combinatorics , struct , partition (number theory) , multiplicity (mathematics) , discrete mathematics , combinatorial proof , property (philosophy) , elementary proof , computer science , mathematical analysis , philosophy , epistemology , programming language
Let n be the set of all distinct ordered pairs ( λ , λ i ), where λ is a partition of n and λ i is a part size of λ . The primary result of this note is a combinatorial proof that the probability that, for a pair ( λ , λ i ) chosen uniformly at random from n , the multiplicity of λ i in λ is 1 tends to 1/2 as n → ∞ . This is inspired by work of Corteel, Pittel, Savage, and Wilf (Random Structures and Algorithms 14 (1999), 185–197). © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007
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