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Left-modular elements

Shu-Chung Liu·Bruce Sagan
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Abstract

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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Shu-Chung Liu, Bruce Sagan. 2000-01-10. Left-modular elements. https://arxiv.org/abs/math/0001055

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