Structure of Binary Sequences
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 \sum_{h=0}^{m} h^{r} {\binom{m}{h}}^{2} in terms of the Stirling numbers of second kind.
Cite
@article{arxiv.math/0109182,
title = {Structure of Binary Sequences},
author = {J. Tharrats},
journal= {arXiv preprint arXiv:math/0109182},
year = {2016}
}
Comments
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.sty v1.2e, all from CTAN, see preamble. To TeX it you have to comment/uncomment 2 lines as indicated in the preamble