====== Thomas Zaslavsky ======

====== Composed Partitions of a Set, With Gain Graphs ======

===== Abstract for the Combinatorics and Number Theory Seminar 2000 November 8 =====

A **composed partition** of a set //V// is a partition of //V// in which each block has a **composition** (an ordered partition) into subblocks. In a //k//-composed partition (sometimes unhappily called a ``generalized partition''), the composition may have empty subblocks, but not more than //k//-1 in a row. The composed and ordinary partitions of a set, like the ordinary partitions, form a geometric lattice (which means they have a nice geometrical representation). The composed partitions of all subsets of a set form a different and even more interesting geometric lattice.

Composed partitions arise from examples of additive gain graphs with symmetric, integral gains. I will explain these gain graphs and how they lead to composed partitions.

This talk will not assume any knowledge of my previous talk, [[abstract.20001018|"Perpendicular Dissections of Euclidean Space, With Gain Graphs"]].