منابع مشابه
Combinatorial entropies and statistics
We examine the combinatorial or probabilistic definition (“Boltzmann’s principle”) of the entropy or cross-entropy function H ∝ lnW or D ∝ − lnP, where W is the statistical weight and P the probability of a given realization of a system. Extremisation of H or D, subject to any constraints, thus selects the “most probable” (MaxProb) realization. If the system is multinomial, D converges asymptot...
متن کاملFindStat - the combinatorial statistics database
The FindStat project provides an online platform for mathematicians, particularly for combinatorialists, to gather information about combinatorial statistics and their relations. As of January 2014, the FindStat database contains 173 statistics on 17 combinatorial collections. The project was initiated by Chris Berg and Christian Stump in 2011 at the Laboratoire de combinatoire et d’informatiqu...
متن کاملCombinatorial Statistics on Alternating Permutations
We consider two combinatorial statistics on permutations. One is the genus. The other, d̂es, is defined for alternating permutations, as the sum of the number of descents in the subwords formed by the peaks and the valleys. We investigate the distribution of d̂es on genus zero permutations and Baxter permutations. Our qenumerative results relate the d̂es statistic to lattice path enumeration, the ...
متن کاملCombinatorial Statistics on Non-crossing Partitions
Four statistics, ls, rb, rs, and lb, previously studied on all partitions of { 1, 2, ..., n }, are applied to non-crossing partitions. We consider single and joint distributions of these statistics and prove equidistribution results. We obtain qand p, q-analogues of Catalan and Narayana numbers which refine the rank symmetry and unimodality of the lattice of non-crossing partitions. Two unimoda...
متن کاملOrder Statistics for Decomposable Combinatorial Structures
In this paper we consider the component structure of decomposable combinatorial objects, both labeled and unlabeled, from a probabilistic point of view. In both cases we show that when the generating function for the components of a structure is a logarithmic function, then the joint distribution of the normalized order statistics of the component sizes of a random object of size n converges to...
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ژورنال
عنوان ژورنال: The European Physical Journal B
سال: 2009
ISSN: 1434-6028,1434-6036
DOI: 10.1140/epjb/e2009-00168-5