On the Combinatorial Inverse Monoid IO3

Abstract

In this paper we have compute the Mobius category and the Mobius function of the combinatorial inverse monoid IO3 of all order preserving partial bijections on the set M3={1,2,3}. This category is the reduced standard division category CF(IO3) relative to an idempotent transversal F of the D-classes of IO3. It is a special Mobius category namely a Mobius category in which the values of ?(?) are 1 and –1 for any morphism ? of CF(IO3).