Growth partition functions for cancellative infinite monoids

Details Growth partition functions for cancellative infinite monoids Growth partition functions for cancellative infinite monoids

2010-09-30

arxiv.org/abs/1009.6076v2

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 $\omega_{\Gamma,G}$.

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