Partitions and their lattices

Details Partitions and their lattices Partitions and their lattices

2006-04-09

arxiv.org/abs/math/0604203v1

Mathematics

Combinatorics

Scientific paper

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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