Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

$ h$-vectors of simplicial cell balls


Author: Satoshi Murai
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
Published electronically: September 27, 2012
MathSciNet review: 3003273
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [Bj1] A. Björner, Posets, regular CW complexes and Bruhat order, European J. Combin. 5 (1984), 7-16. MR 746039 (86e:06002)
  • [Bj2] A. Björner, Topological methods, In: Handbook of Combinatorics, R. Graham, M. Grotschel and L. Lovasz, Eds., Elsevier, Amsterdam, 1995, pp. 1819-1872. MR 1373690 (96m:52012)
  • [BFS] A. Björner, P. Frankl and R.P. Stanley, The number of faces of balanced Cohen-Macaulay complexes and a generalized Macaulay theorem, Combinatorica 7 (1987), 23-34. MR 905148 (89d:52012)
  • [BH] W. Bruns and J. Herzog, Cohen-Macaulay rings, Revised Edition, Cambridge University Press, Cambridge, 1998. MR 1251956 (95h:13020)
  • [Ei] D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Grad. Texts in Math., vol. 150, Springer-Verlag, New York, 1995. MR 1322960 (97a:13001)
  • [Ko] S. Kolins, $ f$-vectors of simplicial posets that are balls, J. Algebraic Combin., to appear.
  • [Ma] M. Masuda, $ h$-vectors of Gorenstein$ ^\ast $ simplicial posets, Adv. Math. 194 (2005), 332-344. MR 2139917 (2006b:52009)
  • [MMP] H. Maeda, M. Masuda and T. Panov, Torus graphs and simplicial posets, Adv. Math. 212 (2007), 458-483. MR 2329309 (2008e:55007)
  • [MR] E. Miller and V. Reiner, Stanley's simplicial poset conjecture, after M. Masuda, Comm. Algebra 34 (2006), 1049-1053. MR 2208116 (2006m:13023)
  • [Mu] S. Murai, Face vectors of simplicial cell decompositions of manifolds, Israel J. Math., to appear.
  • [St1] R.P. Stanley, $ f$-vectors and $ h$-vectors of simplicial posets, J. Pure Appl. Algebra 71 (1991), 319-331. MR 1117642 (93b:06009)
  • [St2] R.P. Stanley, Combinatorics and commutative algebra, Second edition, Progr. Math., vol. 41, Birkhäuser, Boston, 1996. MR 1453579 (98h:05001)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 05E45, 52B05, 13F55

Retrieve articles in all journals with MSC (2010): 05E45, 52B05, 13F55


Additional Information

Satoshi Murai
Affiliation: Department of Mathematical Science, Faculty of Science, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8512, Japan
Email: murai@yamaguchi-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-2012-05674-1
Received by editor(s): May 31, 2011
Received by editor(s) in revised form: July 19, 2011
Published electronically: September 27, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society