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arXiv · 2406.16411

On the Orthogonality of Generalized Pattern Sequences

Shuo Li
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Abstract

The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern sequences, which count the occurrences of a finite number of different patterns in the expansion of positive integers in any integer base, and analyze their partial sums.

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Shuo Li. 2024-06-24. On the Orthogonality of Generalized Pattern Sequences. https://doi.org/10.4204/eptcs.403.29

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