Mathematics – Combinatorics
Scientific paper
2010-04-17
Mathematics
Combinatorics
Scientific paper
The aim of this paper is to develop a theory of finite transformation monoids and in particular to study primitive transformation monoids. We introduce the notion of orbitals and orbital digraphs for transformation monoids and prove a monoid version of D. Higman's celebrated theorem characterizing primitivity in terms of connectedness of orbital digraphs. A thorough study of the module (or representation) associated to a transformation monoid is initiated. In particular, we compute the projective cover of the transformation module over a field of characteristic zero in the case of a transitive transformation or partial transformation monoid. Applications of probability theory and Markov chains to transformation monoids are also considered and an ergodic theorem is proved in this context. In particular, we obtain a generalization of a lemma of P. Neumann, from the theory of synchronizing groups, concerning the partition associated to a transformation of minimal rank.
Steinberg Benjamin
No associations
LandOfFree
A Theory of Transformation Monoids: Combinatorics and Representation Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Theory of Transformation Monoids: Combinatorics and Representation Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Theory of Transformation Monoids: Combinatorics and Representation Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-69785