Frequencies of letters in infinite $k$-balanced sequences
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909774551973888 |
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| author | Dvořáková, Lubomíra Pelantová, Edita |
| author_facet | Dvořáková, Lubomíra Pelantová, Edita |
| contents | Frequency of letters in a symbolic sequence ${\bf u}$ over a finite alphabet is one of the basic characteristics of ${\bf u}$. The notion of $k$-balancedness captures the property that the number of any letter occurring in two arbitrary factors of ${\bf u}$ of equal length differs at most by $k$. For a fixed integer $k$ and alphabet size $d\in \mathbb N$, we discuss possible frequencies of letters in $k$-balanced $d$-ary sequences. For the size $d$ of the alphabet, we introduce the notion of balancedness threshold $BT(d)$ and give an upper bound on it, where $BT(d)$ is the minimum $k$ such that there exists a $k$-balanced sequence over a $d$-letter alphabet for all possible letter frequencies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frequencies of letters in infinite $k$-balanced sequences Dvořáková, Lubomíra Pelantová, Edita Combinatorics 68R15 Frequency of letters in a symbolic sequence ${\bf u}$ over a finite alphabet is one of the basic characteristics of ${\bf u}$. The notion of $k$-balancedness captures the property that the number of any letter occurring in two arbitrary factors of ${\bf u}$ of equal length differs at most by $k$. For a fixed integer $k$ and alphabet size $d\in \mathbb N$, we discuss possible frequencies of letters in $k$-balanced $d$-ary sequences. For the size $d$ of the alphabet, we introduce the notion of balancedness threshold $BT(d)$ and give an upper bound on it, where $BT(d)$ is the minimum $k$ such that there exists a $k$-balanced sequence over a $d$-letter alphabet for all possible letter frequencies. |
| title | Frequencies of letters in infinite $k$-balanced sequences |
| topic | Combinatorics 68R15 |
| url | https://arxiv.org/abs/2509.05812 |