Shellable Nonpure Complexes and Posets. Ii
نویسنده
چکیده
This is a direct continuation of Shellable Nonpure Complexes and Posets. I, which appeared in Transactions of the American Mathematical Society 348 (1996), 1299-1327. 8. Interval-generated lattices and dominance order In this section and the following one we will continue exemplifying the applicability of lexicographic shellability to nonpure posets. Let F = {I1, I2, . . . , In} be a family of intervals of integers, by which is meant sets of the form [a, b] = {a, a + 1, . . . , b}, a ≤ b. We assume that there are no containments among these intervals, and that they are ordered so that their left and right endpoints are increasing. Let L(F) be the lattice of all sets that are unions of subfamilies of F , ordered by inclusion. Such interval-generated lattices L(F) were introduced and studied by Greene [G]. Define an edge-labeling λ of L(F) as follows. If A → B is a covering and a = max(B \A), then λ(A→ B) = { −a, if (a+ 1) ∈ A and a is the left endpoint of some I ∈ F ,
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Shellable Nonpure Complexes and Posets. I
The concept of shellability of complexes is generalized by deleting the requirement of purity (i.e., that all maximal faces have the same dimension). The usefulness of this level of generality was suggested by certain examples coming from the theory of subspace arrangements. We develop several of the basic properties of the concept of nonpure shellability. Doubly indexed f -vectors and h-vector...
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