Josef Rukavicka

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20172026

most citedOn Number of Rich Words

8 citations · 28 across the 18 of their papers we have counts for

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11 papers · 1 filter

math.CO2026

A lower bound on the density of prefixes with maximal palindromic length

Josef Rukavicka

The palindromic length $P L (u)$ of a nonempty finite word $u$ is the least number of nonempty palindromes whose concatenation is $u$ . For an infinite word $w$ , let $P_{w} (n)$ be the n…

math.CO2025

Subexponential upper bound on the number of rich words

Josef Rukavicka

Let $R_{q} (n)$ denote the number of rich words of length $n$ over a fixed alphabet of size $q \geq 2$ . It is known that $R_{q} (n)^{1/ n} \to 1$ . We establish a nonrecursive subexponential u…

math.CO2024

Palindromic length of infinite aperiodic words

Josef Rukavicka

The palindromic length of the finite word $v$ is equal to the minimal number of palindromes whose concatenation is equal to $v$ . It was conjectured in 2013 that for every infinite…

math.CO2022

Property of upper bounds on the number of rich words

Josef Rukavicka

A finite word $w$ is called \emph{rich} if it contains $∣ w ∣ + 1$ distinct palindromic factors including the empty word. Let $q \geq 2$ be the size of the alphabet. Let $R (n)$ …

math.CO2022

Upper bound for the number of privileged words

Josef Rukavicka

A non-empty word $w$ is a \emph{border} of a word $u$ if $∣ w ∣ < ∣ u ∣$ and $w$ is both a prefix and a suffix of $u$ . A word $u$ is \emph{privileged} if $\vert u\vert\…

math.CO2021★ 2 cited

Palindromic factorization of rich words

Josef Rukavicka

A finite word $w$ is called \emph{rich} if it contains $∣ w ∣ + 1$ distinct palindromic factors including the empty word. For every finite rich word $w$ there are distinct non…

math.CO2021★ 3 cited

Palindromic Length and Reduction of Powers

Josef Rukavicka

Given a nonempty finite word $v$ , let $P L (v)$ be the palindromic length of $v$ ; it means the minimal number of palindromes whose concatenation is equal to $v$ . Let $v^{R}$ denote the…

math.CO2019★ 2 cited

Construction Of A Rich Word Containing Given Two Factors

Josef Rukavicka

A finite word $w$ with $∣ w ∣ = n$ contains at most $n + 1$ distinct palindromic factors. If the bound $n + 1$ is attained, the word $w$ is called \emph{rich}. Let $\Factor(w)$ be…

math.CO2018★ 6 cited

Upper Bound for Palindromic and Factor Complexity of Rich Words

Josef Rukavicka

A finite word $w$ of length $n$ contains at most $n + 1$ distinct palindromic factors. If the bound $n + 1$ is attained, the word $w$ is called rich. An infinite word $w$ is called ric…

math.CO2017

Bijections in de Bruijn Graphs

Josef Rukavicka

A T-net of order $m$ is a graph with $m$ nodes and $2 m$ directed edges, where every node has indegree and outdegree equal to $2$ . (A well known example of T-nets are de Bruijn grap…

math.CO2017★ 8 cited

On Number of Rich Words

Josef Rukavicka

Any finite word $w$ of length $n$ contains at most $n + 1$ distinct palindromic factors. If the bound $n + 1$ is reached, the word $w$ is called rich. The number of rich words of lengt…