The rank of the inverse semigroup of partial automorphisms on a finite fence

2019/03/25 by Jörg Koppitz, Koppitz, J., Tiwadee Musunthia +1
Computer Science · #20M18 #20M20 #FOS: Mathematics #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1903.10155

openalex publication_date 2019/03/25 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28

Abstract

A fence is a particular partial order on a (finite) set, close to the linear order. In this paper, we calculate the rank of the semigroup FI_n of all order-preserving partial injections on an n-element fence. In particular, we provide a minimal generating set for FI_n. In the present paper, n is odd since this problem for even n was already solved by I. Dimitrova and J. Koppitz.

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