On semi-Eulerian partially ordered sets with boundary

Authors:
Beifang Chen;Mankwong Lau
Affiliations:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Venue:
European Journal of Combinatorics
Year:
2003

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Abstract

Eulerian posets are motivated by the posets from triangulations of spheres; semi-Eulerian posets are motivated by the posets from triangulations of manifolds. Motivated by investigation (Proc. Natl. Acad. Sci. USA 95 (1998) 9093; Adv. Appl. Math. 19 (1997) 144; J. Combin. Theory Ser. A 85 (1999) 1; Adv. Appl. Math. 21 (1998) 22) on the number of faces of triangulations of manifolds with boundary, we introduce semi-Eulerian posers with boundary in this paper, and generalize the reciprocity laws, the Dehn-Sommerville equations, and the combinatorial Alexander duality to semi-Eulerian posets with boundary.