Combinatorics on Brauer-type semigroups
David Larsson · 2006
The Brauer semigroup Bn of partitions of a 2n-element set into two-element subsets, can be generalized in various ways. For example we may consider arbitrary partitions to obtain the semigroup Cn. The visualization of elements of these semigroups as chips leads us to the Temperley-Lieb semigroup TLn and its analogue TLCn. We study combinatorial properties of these four semigroups. For example, we describe Green’s relations for these semigroups and we count the size of the various equivalence classes. We also study idempotents and the corresponding maximal subgroups in these semigroups, and give some formulas for calculating the number of idempotents. Finally we study regularity and inverse elements of our four semigroups. 1