✦ LIBER ✦

Left-Modular Elements of Lattices

✍ Scribed by Shu-Chung Liu; Bruce E. Sagan

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 168 KB
Volume: 91
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3102

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✦ Synopsis

Left-modularity is a concept that generalizes the notion of 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 theorem [6] about the partial factorization of / in a geometric lattice. Both formulae provide us with inductive proofs for Blass and Sagan's theorem [2] about the total factorization of / in LL lattices. The characteristic polynomials and the Mo bius functions of non-crossing partition lattices and shuffle posets are computed as examples.

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