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The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
5
votes
Is an Eulerian lattice shellable?
I think that the answer to your question ought to be "not always".
There are examples of non-shellable balls and spheres. A very readable account of these, together with some of the history, can b …
4
votes
Positivity of the alternating sum of indices for boolean interval of finite groups
UPDATE: The original poster of the question, together with Mamta Balodi, have shown that the labeling I suggest below is an EL-labeling if and only if group (product) complements coincide with lattic …