Lattice aggregations of boxes and symmetric functions

Abstract

We introduce two lattice growth models: aggregation of $l$-dimensional boxes and aggregation of partitions with $l$ parts. We describe properties of the models: the parameter set of aggregations, the moments of the random variable of the number of growth directions, asymptotical behavior of proportions of the most frequent transitions of two- and three-dimensional self-aggregations.

arXiv comment25 pages, 15 figures