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Partition algebras with non-zero parameters are cellularly stratified andthus have the features of both cellular algebras and stratified algebras. Also,partition algebras form a tower of algebras. In this paper, we provide adiagrammatic approach to study the branching rules for cell modules on a towerof the partition algebras. This also allows us to calculate the structureconstants of the Grothendieck ring of the tower.

Branching rules for cell modules on a tower of the partition algebras