Rational Growth of a Class of Inverse Semigroups


J. Lau


Research Report 96-31
Date: August 1996, revised January 1997


We give a necessary condition for a finitely presented Rees quotient of a free inverse semigroup to have rational growth. Using related techniques we give a new proof that non-monogenic free inverse semigroups have irrational growth. A new criterion for polynomial growth is proved and used to show that polynomial growth implies rational growth. However we give an example of such a semigroup which has rational and exponential growth.

Key phrases

rational growth. polynomial growth. inverse semigroups.

AMS Subject Classification (1991)

Primary: 20M05
Secondary: 20M18, 20M99


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