Partitions and their lattices

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Publication date: 9 April 2006

Abstract: Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative numbers. Partitions are then tabulated into lattices and some properties of these lattices are studied. There appears a new identity counting Ferrers graphs packed consecutively into isoscele form. The lattices form the base for tabulating combinatorial identities.

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