论文标题
$ m $ -tamari和bicambrian lattices上的rotmotion
Rowmotion on $m$-Tamari and BiCambrian Lattices
论文作者
论文摘要
托马斯（Thomas）和威廉姆斯（Williams）猜想，行动的行为$（a，b）$ -Tamari lattice的订单$ a+b-1 $。我们构建了一个模棱两可的培训，该二像bivation证明了当$ b \ equiv 1 \ pmod a $时证明了这一猜想；实际上，在这种情况下，我们确定了行模的整个轨道结构，表明它表现出循环筛分现象。我们还表明，下级统计量对于此动作是同质的。从不同的角度来看，我们考虑了划船对Barnard和Reading的双打晶格的作用。解决了托马斯和威廉姆斯的不同猜想，我们证明，如果$ c $是偶然型coxeter型组的两部分coxeter元素，那么$ c $ bicambrian lattice上的rowmotion的轨道结构与$ rattion $ post $ post $ post post post post post post post post的轨道结构相同。
Thomas and Williams conjectured that rowmotion acting on the rational $(a,b)$-Tamari lattice has order $a+b-1$. We construct an equivariant bijection that proves this conjecture when $b\equiv 1\pmod a$; in fact, we determine the entire orbit structure of rowmotion in this case, showing that it exhibits the cyclic sieving phenomenon. We additionally show that the down-degree statistic is homomesic for this action. In a different vein, we consider the action of rowmotion on Barnard and Reading's biCambrian lattices. Settling a different conjecture of Thomas and Williams, we prove that if $c$ is a bipartite Coxeter element of a coincidental-type Coxeter group $W$, then the orbit structure of rowmotion on the $c$-biCambrian lattice is the same as the orbit structure of rowmotion on the lattice of order ideals of the doubled root poset of type $W$.
