Some Notes on Pairs in Binary Strings
Combinatorics
2016-09-06 v1
Abstract
Seth (Mathematics Stack Exchange, http://math.stackexchange.com/q/1812699) posed a problem that is equivalent to the following: how many binary strings of length n have exactly k pairs of consecutive 0s and exactly m pairs of consecutive 1s, where the first and last bits are considered as being consecutive? In this paper, we provide a closed form solution which also solves a related problem with some interesting connections to other combinatorial sequences.
Cite
@article{arxiv.1609.00980,
title = {Some Notes on Pairs in Binary Strings},
author = {Jeremy M. Dover},
journal= {arXiv preprint arXiv:1609.00980},
year = {2016}
}
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8 pages