Jumbled Scattered Factors
Pamela Fleischmann, Annika Huch, Melf Kammholz, Tore Ko{\ss}

TL;DR
This paper introduces the concept of jumbled scattered factors, combining ideas from scattered factors and jumbled words, and explores their properties, characterizations, and relations to classical string problems.
Contribution
It defines and characterizes jumbled scattered factors, relating them to longest common subsequence and Simon's congruence, advancing understanding of word factorization with jumbling.
Findings
Characterization of jumbled scattered factors based on the number of jumbled letters
Relation between longest common subsequence and jumbled factors
Analysis of minimal jumbles needed for factorization
Abstract
In this work, we combine the research on (absent) scattered factors with the one of jumbled words. For instance, is an absent scattered factor of but since , a jumbled (or abelian) version of , is a scattered factor, occurs as a jumbled scattered factor in . A \emph{jumbled scattered factor} of a word is constructed by letters of with the only rule that the number of occurrences per letter in is smaller than or equal to the one in . We proceed to partition and characterise the set of jumbled scattered factors by the number of jumbled letters and use the latter as a measure. For this new class of words, we relate the folklore longest common subsequence (scattered factor) to the number of required jumbles. Further, we investigate the smallest possible number of…
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Taxonomy
TopicsRandom Matrices and Applications · semigroups and automata theory · Advanced Combinatorial Mathematics
