Details
| Original language | English |
|---|---|
| Pages (from-to) | 485-503 |
| Number of pages | 19 |
| Journal | Mathematics of computation |
| Volume | 84 |
| Issue number | 291 |
| Publication status | Published - 1 Jan 2015 |
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 H3, while proving that there does not exist a poset satisfying all of the properties in type H4. We do this by exhaustive computer searches for posets having these properties. We further give a realization of the poset of type H3 as restricted roots of type D6, and conjecture a Hilbert polynomial for the q, t-Catalan numbers for type H4.
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Mathematics of computation, Vol. 84, No. 291, 01.01.2015, p. 485-503.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On root posets for noncrystallographic root systems
AU - Cuntz, Michael
AU - Stump, Christian
N1 - Publisher Copyright: © 2014 American Mathematical Society. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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 H3, while proving that there does not exist a poset satisfying all of the properties in type H4. We do this by exhaustive computer searches for posets having these properties. We further give a realization of the poset of type H3 as restricted roots of type D6, and conjecture a Hilbert polynomial for the q, t-Catalan numbers for type H4.
AB - 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 H3, while proving that there does not exist a poset satisfying all of the properties in type H4. We do this by exhaustive computer searches for posets having these properties. We further give a realization of the poset of type H3 as restricted roots of type D6, and conjecture a Hilbert polynomial for the q, t-Catalan numbers for type H4.
UR - http://www.scopus.com/inward/record.url?scp=84930435724&partnerID=8YFLogxK
U2 - 10.1090/s0025-5718-2014-02841-x
DO - 10.1090/s0025-5718-2014-02841-x
M3 - Article
AN - SCOPUS:84930435724
VL - 84
SP - 485
EP - 503
JO - Mathematics of computation
JF - Mathematics of computation
SN - 0025-5718
IS - 291
ER -