Abstract
Crystallization theory has been useful in representing piecewise-linear (PL) manifolds in any dimension as D-regular edge-colored bipartite graphs. PL manifolds are of increasing interest to theoretical physicists as a tool to explore discretized versions of geometry in quantum gravity. We provide here a dictionary and compare quantities which have appeared in two contexts: in the so-called crystallizationtheory of simplicial manifolds (mathematics) and in colored tensor models which are simplicial models in view of providing a quantum version of general relativity (physics).
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