標題: LIMIT BEHAVIOR OF MAXIMA IN GEOMETRIC WORDS REPRESENTING SET PARTITIONS
作者: Fuchs, Michael
Javanian, Mehri
應用數學系
Department of Applied Mathematics
關鍵字: Geometric words;restricted growth property;set partitions;moments;limit laws
公開日期: 1-Oct-2015
摘要: We consider geometric words omega(1) ... omega(n) with letters satisfying the restricted growth property omega(k) <= d max{omega(0), ..., omega(k-1)}, where omega(0) := 0 and d >= 1. For d = 1 these words are in 1-to-1 correspondence with set partitions and for this case, we show that the number of left-to-right maxima (suitable centered) does not converge to a fixed limit law as n tends to infinity. This becomes wrong for d >= 2, for which we prove that convergence does occur and the limit law is normal. Moreover, we also consider related quantities such as the value of the maximal letter and the number of maximal letters and show again non-convergence to a fixed limit law.
URI: http://dx.doi.org/10.2298/AADM150619013F
http://hdl.handle.net/11536/128427
ISSN: 1452-8630
DOI: 10.2298/AADM150619013F
期刊: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
起始頁: 313
結束頁: 331
Appears in Collections:Articles