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 Möbius inversion formula for these intervals, together with further graph-theoretic observations, yield “graphical generalizations” of the sieve formula.
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Received: July 21, 1999 Final version received: November 6, 2001
RID="*"
ID="*" On leave from the Alfréd Rényi Mathematical Institute, Hungarian Academy of Sciences. Partially supported by Hungarian National Foundation for Scientific Research grant no. F032325
Acknowledgments. I wish to thank to Margaret Bayer and Louis Billera for inspiration and many fruitful conversations, and to Douglas West for providing vital graph-theoretic background information.
1991 Mathematics Subject Classification. Primary 05, Secondary 06A8, 06B, 05C40
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Hetyei, G. Graphs and Balanced Simplicial Complexes. Graphs Comb 18, 533–564 (2002). https://doi.org/10.1007/s003730200039
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DOI: https://doi.org/10.1007/s003730200039