Journal article
Random Partitions with Non-negative rth Differences
Advances in applied mathematics, v 27(02-03), pp 298-317
01 Aug 2001
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Abstract
Let Pr(n) be the set of partitions of n with non-negative rth 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 rth 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 and was motivated by a recent identity from the Omega package of G. E. Andrews et al. (European J. Combin., MacMahon's partition analysis. III. The Omega package). To prove this result we use bijective, asymptotic/analytic, and probabilistic combinatorics.
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Details
- Title
- Random Partitions with Non-negative rth Differences
- Creators
- Rod Canfield - Department of Computer Science, University of Georgia, Athens, Georgia, 30602, f1erc@cs.uga.eduf1Sylvie Corteel - Unis (Czechia)Pawel Hitczenko - Drexel University
- Publication Details
- Advances in applied mathematics, v 27(02-03), pp 298-317
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000172251600007
- Scopus ID
- 2-s2.0-0035413450
- Other Identifier
- 991020532098104721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied