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Asymptotic behavior of random heaps
Author(s) -
Hough J. B.
Publication year - 2005
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.20077
Subject(s) - heap (data structure) , mathematics , conjecture , struct , random walk , combinatorics , limit (mathematics) , boundary (topology) , discrete mathematics , mathematical analysis , statistics , computer science , algorithm , programming language
We consider a random walk W n on the locally free group (or equivalently a signed random heap) with m generators subject to periodic boundary conditions. Let #T ( W n ) denote the number of removable elements, which determines the heap's growth rate. We prove that lim n →∞ ( #T ( W n ))/ m ≤ 0.32893 for m ≥ 4. This result disproves a conjecture (due to Vershik, Nechaev and Bikbov [Comm Math Phys 212 (2000), 469–501]) that the limit tends to 1/3 as m → ∞. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005