f-vectors of simplicial posets that are balls
Samuel R. Kolins
DOI: 10.1007/s10801-011-0283-7
Abstract
Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vectors. We also present new methods for constructing poset balls with specific h-vectors. Combining this work with a new result of S. Murai we are able to give a complete characterization of the h-vectors of simplicial poset balls in all even dimensions, as well as odd dimensions less than or equal to five.
Pages: 587–605
Keywords: keywords simplicial poset; $f$-vector; face ring; $h$-vector
Full Text: PDF
References
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2. Kolins, S.: f -vectors of triangulated balls. Discrete Comput. Geom. (2010). doi:
3. Macdonald, I.G.: Polynomials associated with finite cell-complexes. J. Lond. Math. Soc. 4, 181-192 (1971)
4. Masuda, M.: h-vectors of Gorenstein* simplicial posets. Adv. Math. 194, 332-344 (2005)
5. Miller, E., Reiner, V.: Stanley's simplicial poset conjecture, after M. Masuda. Commun. Algebra 34, 1049-1053 (2006)
6. Munkres, J.R.: Topological results in combinatorics. Mich. Math. J. 31, 113-128 (1984)
7. Murai, S.: On h-vectors of simplicial cell balls. Preprint (2011)
8. Murai, S.: Face vectors of simplicial cell decompositions of manifolds. Preprint (2010).
9. Stanley, R.P.: f -vectors and h-vectors of simplicial posets. J. Pure Appl. Algebra 71, 319-331 (1991)
10. Stanley, R.P.: A monotonicity property of h-vectors and h* -vectors. Eur. J. Comb. 14, 251-258 (1993)
11. Stanley, R.P.: Combinatorics and Commutative Algebra, 2nd edn. Progress in Mathematics, vol. 41.
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