Concepedia

Avoiding Patterns in the Abelian Sense

James D. Currie, Václav Linek

Canadian Journal of Mathematics · 2001 · 18 citations · 13 references

Open access

Concepts

Abelian SenseCombinatorics On WordAbelian AvoidanceMorphologyUniversal AlgebraLanguage StudiesSemanticsPattern MatchingLinguisticsLetter Patterns

Abstract

Abstract We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some properties of ω-words avoiding these patterns.

References

13

Symbolic Dynamics

Marston Morse, Gustav A. Hedlund · American Journal of Mathematics · 1938 · 427 citations

Some unsolved problems.

Paul Erdős · The Michigan Mathematical Journal · 1957 · 333 citations · Full text

P Versus Np Problem, Problem Diagnosis, Discrete Mathematics +2

Avoidable patterns in strings of symbols

Dwight Bean, Andrzej Ehrenfeucht, George F. McNulty · Pacific Journal of Mathematics · 1979 · 305 citations · Full text

Finite String, Combinatorics On Word, Topological Semigroups +13

Non-repetitive sequences

P. A. B. Pleasants · Mathematical Proceedings of the Cambridge Philosophical Society · 1970 · 140 citations

Combinatorics On Word, Non-repetitive Sequence, Discrete Mathematics +2

BLOCKING SETS OF TERMS

Mathematics of the USSR-Sbornik · 1984 · 136 citations

Combinatorics On Word, Finite Number, Terminology Management +10