文摘
The Ish arrangement was introduced by Armstrong to give a new interpretation of the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0097316516300991&_mathId=si1.gif&_user=111111111&_pii=S0097316516300991&_rdoc=1&_issn=00973165&md5=5d1b79727b2913be85202db1b1d430cc" title="Click to view the MathML source">q,tclass="mathContainer hidden">class="mathCode">-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement and posed some problems. One of them is whether the Ish arrangement is a free arrangement or not. In this paper, we verify that the Ish arrangement is supersolvable and hence free. Moreover, we give a necessary and sufficient condition for the deleted Ish arrangement to be free.