The rank of the inverse semigroup of partial automorphisms on a finite fence
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 FIn of all order-preserving partial injections on an n-element fence. In particular, we provide a minimal generating set for FIn. 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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