Abstract
SynopsisLet E be the set of idempotents in Sn, the semigroup of all singular selfmaps of {1,…, n}. For each α in Sn, there is a unique (κ(α)≧1 such that αψEκ,(α). It is known that κ(α)≦ n + cycl α -fix α, where cyclα is the number of cyclic orbits of a and fix α is the number of fixed points. Equality holds only in the case where a is of rank n – 1. An improved upper bound is obtained for κ(α), applying to elements of arbitrary rank. A lower bound is obtained also.
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Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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