Structure of Binary Sequences

2001/09/24 by Tharrats, J.
#05A15 (Primary) 11B39 #11B73 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0109182

Abstract

The distribution of a given sequence in the set of all sequences with n ones and m = M - n zeros are found by relating the problem to the partitions of a natural number in m natural summands, taking into account the order. The formulas obtained have many applications both in Physics and Mathematics. Examples discussed in the present paper are: non Markovian chains, partition functions of binary alloys and Ising magnets, generalized Kaplansky lemma, generalized Fibonacci numbers and a general expansion of ∑_h=0^m h^r \binommh² in terms of the Stirling numbers of second kind.

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