Discrete & Computational Geometry

, Volume 33, Issue 3, pp 535–545

Obstructions to Shiftedness


DOI: 10.1007/s00454-004-1103-9

Cite this article as:
Klivans, C. Discrete Comput Geom (2005) 33: 535. doi:10.1007/s00454-004-1103-9


In this paper we show results on the combinatorial properties of shifted simplicial complexes. We prove two intrinsic characterization theorems for this class. The first theorem is in terms of a generalized vicinal preorder. It is shown that a complex is shifted if and only if the preorder is total. Building on this we characterize obstructions to shiftedness and prove there are finitely many in each dimension. In addition, we give results on the enumeration of shifted complexes and a connection to totally symmetric plane partitions.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Computing and Information Science, Cornell University, Ithaca, NY 14853USA

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