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Transactions of the American Mathematical Society

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

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Correction to “Combinatorics and geometry of power ideals”: Two counterexamples for power ideals of hyperplane arrangements
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by Federico Ardila and Alexander Postnikov PDF
Trans. Amer. Math. Soc. 367 (2015), 3759-3762 Request permission

Abstract:

We disprove Holtz and Ron’s conjecture that the power ideal $C_{\mathcal {A},-2}$ of a hyperplane arrangement $\mathcal {A}$ (also called the internal zonotopal space) is generated by $\mathcal {A}$-monomials. We also show that, in contrast with the case $k \geq -2$, the Hilbert series of $C_{\mathcal {A},k}$ is not determined by the matroid of $\mathcal {A}$ for $k \leq -6$.
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Additional Information
  • Federico Ardila
  • Affiliation: Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, California 94110
  • MR Author ID: 725066
  • Email: federico@sfsu.edu
  • Alexander Postnikov
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
  • Email: apost@math.mit.edu
  • Received by editor(s): November 7, 2012
  • Received by editor(s) in revised form: January 4, 2013
  • Published electronically: January 15, 2015
  • Additional Notes: The first author was supported in part by NSF Award DMS-0801075 and CAREER Award DMS-0956178.
    The second author was supported in part by NSF CAREER Award DMS-0504629.
  • © Copyright 2015 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 3759-3762
  • MSC (2010): Primary 05A15, 05B35, 13P99, 41A15, 52C35
  • DOI: https://doi.org/10.1090/S0002-9947-2015-06071-1
  • MathSciNet review: 3314823