Josef Rukavicka

activity

20172026

most citedOn Number of Rich Words

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

collaborators

19 papers

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…

cs.FL2023

Restivo Salemi property for $α$ -power free languages with $α \geq 5$ and $k \geq 3$ letters

Josef Rukavicka

In 2009, Shur published the following conjecture: Let $L$ be a power-free language and let $e (L) \subseteq L$ be the set of words of $L$ that can be extended to a bi-infinite word r…

cs.FL2023

Note on dissecting power of regular languages

Josef Rukavicka

Let $c > 1$ be a real constant. We say that a language $L$ is $c$ -\emph{constantly growing} if for every word $u \in L$ there is a word $v \in L$ with $\vert u\vert<\vert v\vert\leq c+…

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\…

cs.FL2022

Construction of a bi-infinite power free word with a given factor and a non-recurrent letter

Josef Rukavicka

Let $L_{k, α}^{Z}$ denote the set of all bi-infinite $α$ -power free words over an alphabet with $k$ letters, where $α$ is a positive rational number and $k$ is positive int…

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.PR2021

Secretary problem and two almost the same consecutive applicants

Josef Rukavicka

We present a new variant of the secretary problem. Let $A$ be a totally ordered set of $n$ \emph{applicants}. Given $P \subseteq A$ and $x \in A$ , let $rr(P,x)=\vert\{z\in P \mid z\l…

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…

cs.FL2020

Dissecting power of intersection of two context-free languages

Josef Rukavicka

We say that a language $L$ is \emph{constantly growing} if there is a constant $c$ such that for every word $u \in L$ there is a word $v \in L$ with $\vert u\vert<\vert v\vert\leq c+…

cs.FL2020★ 2 cited

Palindromic Length of Words with Many Periodic Palindromes

Josef Rukavicka

The palindromic length $PL (v)$ of a finite word $v$ is the minimal number of palindromes whose concatenation is equal to $v$ . In 2013, Frid, Puzynina, and Zamboni conjecture…

cs.DM2019★ 2 cited

Upper bound for the number of closed and privileged words

Josef Rukavicka

A non-empty word $w$ is a border of the word $u$ if $∣ w ∣ < ∣ u ∣$ and $w$ is both a prefix and a suffix of $u$ . A word $u$ with the border $w$ is closed if $u$ has ex…

cs.DM2019★ 3 cited

A Unique Extension of Rich Words

Josef Rukavicka

A word $w$ is called rich if it contains $∣ w ∣ + 1$ palindromic factors, including the empty word. We say that a rich word $w$ can be extended in at least two ways if there are two d…

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…

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

Subexponential upper bound on the number of rich words

Palindromic length of infinite aperiodic words

Restivo Salemi property for α-power free languages with α≥5 and k≥3 letters

Note on dissecting power of regular languages

Property of upper bounds on the number of rich words

Upper bound for the number of privileged words

Construction of a bi-infinite power free word with a given factor and a non-recurrent letter

Palindromic factorization of rich words

Secretary problem and two almost the same consecutive applicants

Palindromic Length and Reduction of Powers

Dissecting power of intersection of two context-free languages

Palindromic Length of Words with Many Periodic Palindromes

Upper bound for the number of closed and privileged words

A Unique Extension of Rich Words

Construction Of A Rich Word Containing Given Two Factors

Upper Bound for Palindromic and Factor Complexity of Rich Words

Bijections in de Bruijn Graphs

On Number of Rich Words

Restivo Salemi property for $α$ -power free languages with $α \geq 5$ and $k \geq 3$ letters