m-Nearly k-Universal Words – Investigating Simon Congruence

Pamela Fleischmann
Kiel University (CAU)

Date(s) : 09/01/2023   iCal
15 h 00 min - 16 h 00 min

Determining the index of the Simon congruence is a long outstanding open problem. Two words and are called Simon congruent if they have the same set of scattered factors, which are parts of the word in the correct order but not necessarily consecutive, e.g., oath is a scattered factor of logarithm. Following the idea of scattered factor -universality, we investigate -nearly -universality, i.e., words where scattered factors of length are absent, w.r.t. Simon congruence. We present a full characterisation as well as the index of the congruence for , , and . Moreover, we present a characterisation of the universality of repetitions.

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