Left-modular elements

Details Left-modular elements Left-modular elements

2000-01-10

arxiv.org/abs/math/0001055v1

J. Combin. Theory (A) 91 (2000), 369-385.

Mathematics

Combinatorics

20 pages, 1 figure

Scientific paper

Left-modularity is a concept that generalizes modularity in lattice theory. In this paper, we give a characterization of left-modular elements and derive two formulae for the characteristic polynomial of a lattice with such an element, one of which generalizes Stanley's Partial Factorization Theorem for a geometric lattice with a modular element. Both formulae provide us with inductive proofs of Blass and Sagan's Total Factorization Theorem for LL lattices. The characteristic polynomials and Mobius functions of non-crossing partition lattices and shuffle posets are computed as examples.

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