A basis construction of the extended Catalan and Shi arrangements of the type A2
Copyright policy )A basis construction of the extended Catalan and Shi arrangements of the type A2
In [9], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method, Yoshinaga proved the freeness of the extended Catalan and Shi arrangements in [11]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements. In this paper, we give the first explicit construction of them when the root system is of the type $A_2$.
- Hokkaido University Japan
- Kyushu University Japan
- Hokkaido Bunkyo University Japan
Relations with arrangements of hyperplanes, FOS: Mathematics, 32S22, 20F55, 13N15, Mathematics - Combinatorics, Combinatorics (math.CO), hyperplane arrangement, Catalan arrangement, Shi arrangement
Relations with arrangements of hyperplanes, FOS: Mathematics, 32S22, 20F55, 13N15, Mathematics - Combinatorics, Combinatorics (math.CO), hyperplane arrangement, Catalan arrangement, Shi arrangement
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!