Left-modular Elements
نویسنده
چکیده
Left-modularity [2] is a more general concept than modularity in lattice theory. In this paper, we give a characterization of left-modular elements and demonstrate two formulae for the characteristic polynomial of a lattice with such an element, one of which generalizes Stanley’s Partial Factorization Theorem. Both formulae provide us with inductive proofs for Blass and Sagan’s Total Factorization Theorem for LL lattices. The characteristic polynomials and the Möbius functions of non-crossing partition lattices and shuffle posets are computed as examples.
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