### Abstract

A subset U of a set S with a binary operation is called avoidable if S can be partitioned into two subsets A and B such that no element of U can be written as a product of two distinct elements of A or as the product of two distinct elements of B. The avoidable sets of the bicyclic inverse semigroup are classified.

Original language | English (US) |
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Pages (from-to) | 273-288 |

Number of pages | 16 |

Journal | Ars Combinatoria |

Volume | 77 |

State | Published - Oct 2005 |

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### Keywords

- Additive partition
- Avoidable set
- Bicyclic inverse semigroup
- Bipartite graph

### ASJC Scopus subject areas

- Mathematics(all)