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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Subdivisions and local $h$-vectors
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by Richard P. Stanley PDF
J. Amer. Math. Soc. 5 (1992), 805-851 Request permission


In Part I a general theory of $f$-vectors of simplicial subdivisions (or triangulations) of simplicial complexes is developed, based on the concept of local $h$-vector. As an application, we prove that the $h$-vector of a Cohen-Macaulay complex increases under “quasi-geometric” subdivision, thus establishing a special case of a conjecture of Kalai and this author. Techniques include commutative algebra, homological algebra, and the intersection homology of toric varieties. In Part II we extend the work of Part I to more general situations. First a formal generalization of subdivision is given based on incidence algebras. Special cases are then developed, in particular one based on subdivisions of Eulerian posets and involving generalized $h$-vectors. Other cases deal with Kazhdan-Lusztig polynomials, Ehrhart polynomials, and a $q$-analogue of Eulerian posets. Many applications and examples are given throughout.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 5 (1992), 805-851
  • MSC: Primary 52B20; Secondary 05E99, 06A07, 13D40, 55U10
  • DOI:
  • MathSciNet review: 1157293