On the semigroup of partial isometries of a finite chain

2010/12/30 by Rotimi Kehinde, Abdullahi Umar, Kehinde, Rotimi +1 · 1 citation
Computer Science · Mathematics · #20M #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20M #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1101.0049

12 pages, 4 tables, submitted to a journal

arxiv created 2010/12/30 · openalex publication_date 2010/12/30 · arxiv updated 2011/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \cal I_n be the symmetric inverse semigroup on X_n = \1, 2,..., n\ and let \cal DP_n and \cal ODP_n be its subsemigroups of partial isometries and of order-preserving partial isometries of X_n, respectively. In this paper we investigate the cycle structure of a partial isometry and characterize the Green's relations on \cal DP_n and \cal ODP_n. We show that \cal ODP_n is a 0-E-unitary inverse semigroup. We also investigate the cardinalities of some equivalences on \cal DP_n and \cal ODP_n which lead naturally to obtaining the order of the semigroups.

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