  This paper presents a novel approach to representing task assignments for
partitioned agents (respectively, tasks) in distributed systems. A partition of
agents (respectively, tasks) is represented by a Young tableau, which is one of
the main tools in studying symmetric groups and combinatorics. In this paper we
propose a task, agent, and assignment tableau in order to represent a task
assignment for partitioned agents (respectively, tasks) in a distributed
system. This paper is concerned with representations of task assignments rather
than finding approximate or near optimal solutions for task assignments. A
Young tableau approach allows us to raise the expressiveness of partitioned
agents (respectively, tasks) and their task assignments.
