2021/05/18 by Akagi, Tooru, Kuhara, Yuki, Mieno, Takuya +4
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.2105.08496
A string w is called a minimal absent word (MAW) for another string T if w does not occur in T but the proper substrings of w occur in T. For example, let Σ= \\mathtta, b, c\ be the alphabet. Then, the set of MAWs for string w = \mathttabaab is \\mathttaaa, aaba, bab, bb, c\. In this paper, we study combinatorial properties of MAWs in the sliding window model, namely, how the set of MAWs changes when a sliding window of fixed length d is shifted over the input string T of length n, where 1 ≤ d < n. We present tight upper and lower bounds on the maximum number of changes in the set of MAWs for a sliding window over T, both in the cases of general alphabets and binary alphabets. Our bounds improve on the previously known best bounds [Crochemore et al., 2020].