Geodesic
$f$-vectors of simplicial posets that are balls
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 4, pp. 587-605.

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Summary: 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.
Keywords: keywords simplicial poset, $f$-vector, face ring, $h$-vector 
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     author = {Kolins, Samuel R.},
     title = {$f$-vectors of simplicial posets that are balls},
     journal = {Journal of Algebraic Combinatorics},
     pages = {587--605},
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     number = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2011__34_4_a7/}
}
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Kolins, Samuel R. $f$-vectors of simplicial posets that are balls. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 4, pp. 587-605. http://geodesic.mathdoc.fr/item/JAC_2011__34_4_a7/