Abstract
We define geometric semilattices, a generalization of geometric lattices. The poset of independent sets of a matroid is another example. We prove several axiomatic and constructive characterizations, for example: geometric semilattices are those semilattices obtained by removing a principal filter from a geometric lattice. We also show that all geometric semilattices are shellable, unifying and extending several previous results.
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Communicated by A. Björner
Partially supported by NSF grant MCS 81-03474.
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Wachs, M.L., Walker, J.W. On geometric semilattices. Order 2, 367–385 (1985). https://doi.org/10.1007/BF00367425
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DOI: https://doi.org/10.1007/BF00367425