arXiv subjects

Palak Pandoh

Publications and source records attributed to Palak Pandoh.

4 recordsLinked to original sources

arXiv2023

Rich Words in the Block Reversal of a Word

The block reversal of a word $w$, denoted by $\mathtt{BR}(w)$, is a generalization of the concept of the reversal of a word, obtained by concatenating the blocks of the word in the reverse order. We characterize non-binary and binary words whose block reversal contains only rich words. We prove that for a binary word $w$, richness of all elements of $\mathtt{BR}(w)$ depends on $l(w)$, the length of the run sequence of $w$. We show that if all elements of $\mathtt{BR}(w)$ are rich, then $2\leq l(w)\leq 8$. We also provide the structure of such words.

math.CO↗

arXiv2021

Counting scattered palindromes in a finite word

We investigate the scattered palindromic subwords in a finite word. We start by characterizing the words with the least number of scattered palindromic subwords. Then, we give an upper bound for the total number of palindromic subwords in a word of length $n$ in terms of Fibonacci number $F_n$ by proving that at most $F_n$ new scattered palindromic subwords can be created on the concatenation of a letter to a word of length $n-1$. We propose a conjecture on the maximum number of scattered palindromic subwords in a word of length $n$ with $q$ distinct letters. We support the conjecture by showing its validity for words where $q\geq \frac{n}{2}$.

cs.DM↗

arXiv2020

Theta palindromes in theta conjugates

A DNA string is a Watson-Crick (WK) palindrome when the complement of its reverse is equal to itself. The Watson-Crick mapping $θ$ is an involution that is also an antimorphism. $θ$-conjugates of a word is a generalisation of conjugates of a word that incorporates the notion of WK-involution $θ$. In this paper, we study the distribution of palindromes and Watson-Crick palindromes, also known as $θ$-palindromes among both the set of conjugates and $θ$-conjugates of a word $w$. We also consider some general properties of the set $C_θ(w)$, i.e., the set of $θ$-conjugates of a word $w$, and characterize words $w$ such that $|C_θ(w)|=|w|+1$, i.e., with the maximum number of elements in $C_θ(w)$. We also find the structure of words that have at least one (WK)-palindrome in $C_θ(w)$.

cs.FL↗

arXiv2019

Palindromes in two-dimensional Words

A two-dimensional ($2$D) word is a $2$D palindrome if it is equal to its reverse and it is an HV-palindrome if all its columns and rows are $1$D palindromes. We study some combinatorial and structural properties of HV-palindromes and its comparison with $2$D palindromes. We investigate the maximum number number of distinct non-empty HV-palindromic sub-arrays in any finite $2$D word, thus, proving the conjecture given by Anisiua et al. We also find the least number of HV-palindromes in an infinite $2$D word over a finite alphabet size $q$.

cs.DM↗