On root posets for noncrystallographic root systems
نویسندگان
چکیده
منابع مشابه
Orbits of Antichains in Certain Root Posets
Building everything from scratch, we give another proof of Propp and Roby’s theorem saying that the average antichain size in any reverse operator orbit of the poset [m] × [n] is mn m+n . It is conceivable that our method should work for other situations. As a demonstration, we show that the average size of antichains in any reverse operator orbit of [m] ×Kn−1 equals 2mn m+2n−1 . Here Kn−1 is t...
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15 صفحه اولShellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems
We prove that the posets of connected components of intersections of toric and elliptic arrangements defined by root systems are EL-shellable and we compute their homotopy type. Our method rests on Bibby’s description of such posets by means of “labeled partitions”: after giving an EL-labeling and counting homology chains for general posets of labeled partitions, we obtain the stated results by...
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There are two notions of the extended affine root systems in the literature which both are introduced axiomatically. One, extended affine root system (SAERS for short), consists only of nonisotropic roots, while the other, extended affine root system (EARS for short), contains certain isotropic roots too. We show that there is a one to one correspondence between (reduced) SEARSs and EARSs. Name...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2014
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2014-02841-x