Mathematics – Group Theory
Scientific paper
2010-09-30
Mathematics
Group Theory
Changed terminology: partition function(s) -> limit partition function(s), Removed douplicate definition in page 12, Added Ack
Scientific paper
We introduce the {\it growth partition function} $Z_{\Gamma,G}(t)$ associate with any cancellative infinite monoid $\Gamma$ with a finite generator system $G$. It is a power series in $t$ whose coefficients lie in integral Lie-like space $\mathcal{L}_{\Z}(\Gamma,G)$ in the configuration algebra associated with the Cayley graph $(\Gamma,G)$. We determine them for homogeneous monoids admitting left greatest common divisor and right common multiple. Then, for braid monoids and Artin monoids of finite type, using that formula, we explicitly determine their limit partition functions $\omega_{\Gamma,G}$.
No associations
LandOfFree
Growth partition functions for cancellative infinite monoids 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 Growth partition functions for cancellative infinite monoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Growth partition functions for cancellative infinite monoids will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-242840