Abstract:A simplicial cell ball is a simplicial poset whose geometric realization is homeomorphic to a ball. Recently, Samuel Kolins gave a series of necessary conditions and sufficient conditions on $h$-vectors of simplicial cell balls, and characterized them up to dimension $6$. In this paper, we extend Kolins’ results. We characterize all possible $h$-vectors of simplicial cell balls in arbitrary dimension.
- A. Björner, Posets, regular CW complexes and Bruhat order, European J. Combin. 5 (1984), no. 1, 7–16. MR 746039, DOI 10.1016/S0195-6698(84)80012-8
- A. Björner, Topological methods, Handbook of combinatorics, Vol. 1, 2, Elsevier Sci. B. V., Amsterdam, 1995, pp. 1819–1872. MR 1373690
- A. Björner, P. Frankl, and R. Stanley, The number of faces of balanced Cohen-Macaulay complexes and a generalized Macaulay theorem, Combinatorica 7 (1987), no. 1, 23–34. MR 905148, DOI 10.1007/BF02579197
- Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
- S. Kolins, $f$-vectors of simplicial posets that are balls, J. Algebraic Combin., to appear.
- Mikiya Masuda, $h$-vectors of Gorenstein$^\ast$ simplicial posets, Adv. Math. 194 (2005), no. 2, 332–344. MR 2139917, DOI 10.1016/j.aim.2004.06.009
- Hiroshi Maeda, Mikiya Masuda, and Taras Panov, Torus graphs and simplicial posets, Adv. Math. 212 (2007), no. 2, 458–483. MR 2329309, DOI 10.1016/j.aim.2006.10.011
- Ezra Miller and Vic Reiner, Stanley’s simplicial poset conjecture, after M. Masuda, Comm. Algebra 34 (2006), no. 3, 1049–1053. MR 2208116, DOI 10.1080/00927870500442005
- S. Murai, Face vectors of simplicial cell decompositions of manifolds, Israel J. Math., to appear.
- Richard P. Stanley, $f$-vectors and $h$-vectors of simplicial posets, J. Pure Appl. Algebra 71 (1991), no. 2-3, 319–331. MR 1117642, DOI 10.1016/0022-4049(91)90155-U
- Richard P. Stanley, Combinatorics and commutative algebra, 2nd ed., Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1996. MR 1453579
- Satoshi Murai
- Affiliation: Department of Mathematical Science, Faculty of Science, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8512, Japan
- MR Author ID: 800440
- Email: firstname.lastname@example.org
- Received by editor(s): May 31, 2011
- Received by editor(s) in revised form: July 19, 2011
- Published electronically: September 27, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Trans. Amer. Math. Soc. 365 (2013), 1533-1550
- MSC (2010): Primary 05E45, 52B05; Secondary 13F55
- DOI: https://doi.org/10.1090/S0002-9947-2012-05674-1
- MathSciNet review: 3003273