English

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}
}

Comments

8 pages

R2 v1 2026-06-22T15:39:38.864Z