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- W2952024306 abstract "An integer array y = y[1..n] is said to be feasible if and only if y[1] = n and, for every i in 2..n, i le i+y[i] le n+1. A string is said to be indeterminate if and only if at least one of its elements is a subset of cardinality greater than one of a given alphabet Sigma; otherwise it is said to be regular. A feasible array y is said to be regular if and only if it is the prefix array of some regular string. We show using a graph model that every feasible array of integers is a prefix array of some (indeterminate or regular) string, and for regular strings corresponding to y, we use the model to provide a lower bound on the alphabet size. We show further that there is a 1-1 correspondence between labelled simple graphs and indeterminate strings, and we show how to determine the minimum alphabet size |Sigma| of an indeterminate string x based on its associated graph Gx. Thus, in this sense, indeterminate strings are a more natural object of combinatorial interest than the strings on elements of Sigma that have traditionally been studied." @default.
- W2952024306 created "2019-06-27" @default.
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- W2952024306 date "2014-06-12" @default.
- W2952024306 modified "2023-09-26" @default.
- W2952024306 title "Indeterminate Strings, Prefix Arrays & Undirected Graphs" @default.
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