On root posets for noncrystallographic root systems
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- by Michael Cuntz and Christian Stump PDF
- Math. Comp. 84 (2015), 485-503 Request permission
Abstract:
We discuss properties of root posets for finite crystallographic root systems, and show that these properties uniquely determine root posets for the noncrystallographic dihedral types and type $H_3$, while proving that there does not exist a poset satisfying all of the properties in type $H_4$. We do this by exhaustive computer searches for posets having these properties. We further give a realization of the poset of type $H_3$ as restricted roots of type $D_6$, and conjecture a Hilbert polynomial for the $q,t$-Catalan numbers for type $H_4$.References
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Additional Information
- Michael Cuntz
- Affiliation: Fachbereich Mathematik, Universität Kaiserslautern, Germany
- Address at time of publication: Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und Physik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Email: cuntz@math.uni-hannover.de
- Christian Stump
- Affiliation: Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und Physik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Address at time of publication: Institut für Mathematik, Freie Universität Berlin, Germany
- MR Author ID: 904921
- ORCID: 0000-0002-9271-8436
- Email: christian.stump@fu-berlin.de
- Received by editor(s): December 5, 2012
- Received by editor(s) in revised form: April 11, 2013, and May 10, 2013
- Published electronically: May 28, 2014
- Additional Notes: Most of the results of this article were achieved at the Leibniz Universität Hannover in summer 2012.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 84 (2015), 485-503
- MSC (2010): Primary 20F55
- DOI: https://doi.org/10.1090/S0025-5718-2014-02841-X
- MathSciNet review: 3266972