m-Nearly k-Universal Words – Investigating Simon Congruence – INSTITUT DE MATHÉMATIQUES DE MARSEILLE

Pamela Fleischmann
Kiel University (CAU)
https://www.tompeteder.org/

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 $u$ and $v$ 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 $k$ -universality, we investigate $m$ -nearly $k$ -universality, i.e., words where $m$ scattered factors of length $k$ are absent, w.r.t. Simon congruence. We present a full characterisation as well as the index of the congruence for $m = 1$ , $2$ , and $3$ . Moreover, we present a characterisation of the universality of repetitions.

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