Abstract
Let Pr(n) be the set of partitions of n with non negative r th differences. Let λ be a partition of an integer n chosen uniformly at random among the set Pr(n) Let d(λ) be a positive r th difference chosen uniformly at random in λ. The aim of this work is to show that for every m ≥ 1, the probability that d(λ) ≥ m approaches the constant m ?1/r as n → ∞ This work is a generalization of a result on integer partitions [7] and was motivated by a recent identity by Andrews, Paule and Riese’s Omega package [3]. To prove this result we use bijective, asymptotic/analytic and probabilistic combinatorics.
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Canfield, R., Corteel, S., Hitczenko, P. (2002). Random Partitions with Non Negative rth Differences. In: Rajsbaum, S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45995-2_16
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DOI: https://doi.org/10.1007/3-540-45995-2_16
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