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Partitions and their lattices

Milan kunz
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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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Milan kunz. 2006-04-09. Partitions and their lattices. https://arxiv.org/abs/math/0604203

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