Formulas for the numbers of sequences containing a given pattern given number of times
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Aleksandr A. Serov
Abstract
Explicit recurrent formulas for the numbers of sequences containing a given pattern given number of times are constructed. These formulas depend on the length of the sequence, the length of the pattern and its period only. By means of these results one may find the distribution of statistics of the NIST overlapping matching test for binary sequences and arbitrary pattern parameters.
Originally published in Diskretnaya Matematika (2020) 32,№4, 120–136 (in Russian).
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Articles in the same Issue
- Contents
- Group service system with three queues and load balancing
- Formulas for the numbers of sequences containing a given pattern given number of times
- On a generalization of class of negative binomial distributions
- Invertible matrices over some quotient rings: identification, generation, and analysis
- On synthesis of reversible circuits consisting of NOT, CNOT, 2-CNOT gates with small number of additional inputs
- Computation of distributions of statistics by means of Markov chains
Articles in the same Issue
- Contents
- Group service system with three queues and load balancing
- Formulas for the numbers of sequences containing a given pattern given number of times
- On a generalization of class of negative binomial distributions
- Invertible matrices over some quotient rings: identification, generation, and analysis
- On synthesis of reversible circuits consisting of NOT, CNOT, 2-CNOT gates with small number of additional inputs
- Computation of distributions of statistics by means of Markov chains
