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On a conjecture by Kalai

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Abstract

We show that monomial ideals generated in degree two satisfy a conjecture by Eisenbud, Green and Harris. In particular, we give a partial answer to a conjecture of Kalai by proving that h-vectors of flag Cohen-Macaulay simplicial complexes are h-vectors of Cohen-Macaulay balanced simplicial complexes.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA

    Giulio Caviglia

  2. Institut de Mathématiques, Universitè de Neuchâtel Bâtiment UniMail, Rue Emile-Argand 11, 2000, Neuchâtel, Switzerland

    Alexandru Constantinescu

  3. Dipartimento di Matematica, Università degli Studi di Genova, Via Dodecaneso 35, 16146, Genova, Italy

    Matteo Varbaro

Authors
  1. Giulio Caviglia
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  2. Alexandru Constantinescu
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  3. Matteo Varbaro
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Corresponding author

Correspondence to Giulio Caviglia.

Additional information

The authors thank the Mathematical Sciences Research Institute, Berkeley CA, where this work was done, for support and hospitality during Fall 2012.

The work of the first author was supported by a grant from the Simons Foundation (209661 to G. C.).

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Caviglia, G., Constantinescu, A. & Varbaro, M. On a conjecture by Kalai. Isr. J. Math. 204, 469–475 (2014). https://doi.org/10.1007/s11856-014-1115-y

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  • DOI: https://doi.org/10.1007/s11856-014-1115-y

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