We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac--Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function. The latter is...
We investigate the compatibility of the set of fully commutative elements of a Coxeter
group with the various types of Kazhdan-Lusztig cells using a canonical basis for a
generalized version of the Temperley-Lieb algebra.
Motivated by structured parasite populations in aquaculture we consider a class of
size-structured population models, where individuals may be recruited into the population
with distributed states at birth. The mathematical model which describes the evolution of
such a population is a first-order nonlinear partial integro-differential equation of
hyperbolic type. First, we use positive perturbation arguments and utilise results from
the spectral...
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