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- W2725918824 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." @default.
- W2725918824 created "2017-07-14" @default.
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- W2725918824 date "2017-07-07" @default.
- W2725918824 modified "2023-09-27" @default.
- W2725918824 title "Binary strings of length $n$ with $x$ zeros and longest $k$-runs of zeros" @default.
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