论文标题
通过SB标签
Poset topology of $s$-weak order via SB-labelings
论文作者
论文摘要
CEBALLOS和PONS在某些标签树上的部分订单上对排列的弱点概括，从而引入了一类新的晶格，称为$ s $ weak Order。他们还通过定义了$ s $ weak订单的特定Sublattice（称为$ S $ -Tamari lattice），从而概括了Tamari晶格。我们证明，$ s $ weak Order和$ s $ -tamari晶格的每个开放间隔的同质类型是球或球。我们通过给出$ S $ weak订单和$ s $ tamari lattice的一种边缘标签，称为SB标签。我们表征了哪些间隔是同等的，等于球体，哪些间隔等于球。我们还确定了产生球的间隔的球的尺寸。
Ceballos and Pons generalized weak order on permutations to a partial order on certain labeled trees, thereby introducing a new class of lattices called $s$-weak order. They also generalized the Tamari lattice by defining a particular sublattice of $s$-weak order called the $s$-Tamari lattice. We prove that the homotopy type of each open interval in $s$-weak order and in the $s$-Tamari lattice is either a ball or sphere. We do this by giving $s$-weak order and the $s$-Tamari lattice a type of edge labeling known as an SB-labeling. We characterize which intervals are homotopy equivalent to spheres and which are homotopy equivalent to balls; we also determine the dimension of the spheres for the intervals yielding spheres.
