Binary strings of length $n$ with $x$ zeros and longest $k$-runs of zeros

Monimala Nej; A. Satyanarayana Reddy

paper

Binary strings of length $n$ with $x$ zeros and longest $k$ -runs of zeros

arXiv:1707.02187

Abstract

In this paper, we study $F_{n} (x, k)$ , the number of binary strings of length $n$ containing $x$ zeros and a longest subword of $k$ zeros. A recurrence relation for $F_{n} (x, k)$ is derived. We expressed few known numbers like Fibonacci, triangular, number of binary strings of length $n$ without $r$ -runs of ones and number of compositions of $n + 1$ with largest summand $k + 1$ in terms of $F_{n} (x, k) .$ Similar results and applications were obtained for F $_{n} (x, k),$ the number of all palindromic binary strings of length $n$ containing $x$ zeros and longest $k$ -runs of zeros.

18 pages

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Exponents of primitive symmetric companion matrices

Binary strings of length n with x zeros and longest k-runs of zeros

Abstract

References in corpus (1)

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Binary strings of length $n$ with $x$ zeros and longest $k$ -runs of zeros