Structure of Binary Sequences

Details Structure of Binary Sequences Structure of Binary Sequences

2001-09-24

arxiv.org/abs/math/0109182v1

Mathematics

Combinatorics

29 pages, 0 figures. LaTeX2e (2000/06/01), uses amsart.cls v2.08, dcolumn.sty v1.05, epic.sty v1.2, eepicemu.sty v1.1a, float.

Scientific paper

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 \sum_{h=0}^{m} h^{r} {\binom{m}{h}}^{2} in terms of the Stirling numbers of second kind.

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