$α$-$β$-Factorization and the Binary Case of Simon's Congruence

no code implementations • 25 Jun 2023 • Pamela Fleischmann, Jonas Höfer, Annika Huch, Dirk Nowotka

In 1991 H\'ebrard introduced a factorization of words that turned out to be a powerful tool for the investigation of a word's scattered factors (also known as (scattered) subwords or subsequences).

m-Nearly k-Universal Words -- Investigating Simon Congruence

no code implementations • 16 Feb 2022 • Pamela Fleischmann, Lukas Haschke, Annika Huch, Annika Mayrock, Dirk Nowotka

We present a full characterisation as well as the index of the congruence for $m=1$.