Abstract
We introduce for each directed graph G on n vertices a generalized notion of shellability of balanced (n−1)-dimensional simplicial complexes. In all cases, the closed cone generated by the flag f-vectors of all G-shellable complexes turns out to be an orthant, and we obtain similar descriptions for certain intersections of G-shellability classes. Our results depend in part on the fact that every interval of a partial order induced by leaks along the edges of a graph is an upper semidistributive lattice. The Mobius inversion formula for these intervals, together with further graph-theoretic observations, yield “graphical generalizations” of the sieve formula.
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