On the least number of palindromes in two-dimensional words

Mahalingam, Kalpana; Pandoh, Palak; Krithivasan, Kamala

doi:10.1016/j.tcs.2019.06.030

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Block Reversal Of Binary Words1

Introduction1

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2024

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Cited by 7 publications

(2 citation statements)

References 22 publications

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“…Mahalingam et al ( [19]) characterized words w such that P (w) = 8. They proved that a binary word w has 8 palindromic factors iff w is of the form u…”

Section: Block Reversal Of Binary Wordsmentioning

confidence: 99%

Rich Words in the Block Reversal of a Word

Mahalingam¹,

Maity²,

Pandoh³

2023

Preprint

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The block reversal of a word w, denoted by 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 BR(w) depends on l(w), the length of the run sequence of w. We show that if all elements of BR(w) are rich, then 2 ≤ l(w) ≤ 8. We also provide the structure of such words.

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“…Mahalingam et al ( [19]) characterized words w such that P (w) = 8. They proved that a binary word w has 8 palindromic factors iff w is of the form u…”

Section: Block Reversal Of Binary Wordsmentioning

confidence: 99%

Rich Words in the Block Reversal of a Word

Mahalingam¹,

Maity²,

Pandoh³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…[3]. The maximum and the least number of 2D palindromic sub-arrays in a given array was studied in [2,15] and [16], respectively. Palindromic subsequences, i.e., scattered palindromic subwords, in words were studied recently in [4,10].…”

Section: Introductionmentioning

confidence: 99%

Counting scattered palindromes in a finite word

Mahalingam¹,

Pandoh²

2021

Preprint

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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 Fn by proving that at most Fn 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 ≥ n 2 .

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Palindromes in involutive Fibonacci arrays

Blasiyus,

Christy

2024

J Supercomput

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On the least number of palindromes in two-dimensional words

Cited by 7 publications

References 22 publications

Rich Words in the Block Reversal of a Word

Rich Words in the Block Reversal of a Word

Counting scattered palindromes in a finite word

Palindromes in involutive Fibonacci arrays

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