论文标题
梯形posets的行轨道
Rowmotion Orbits of Trapezoid Posets
论文作者
论文摘要
RowMotion是一个可逆操作员，对POSET的顺序理想，已广泛研究，并且对矩形Poset已被充分理解。在本文中，我们表明，在矩形和梯形posets的秩序理想之间，行李均与hamaker，patrias，pechenik和Williams的两者进行了均衡，从而确认霍普金斯的猜想表明矩形和梯形Posets具有相同的Rowmotion Orbit Orbit Orbit结构。我们证明这是$ k $ -jeu-de-taquin和（弱）$ k $ -kknuth等价tableaux的主要工具。我们将几乎$ $ $ $ $ $ $ $ tableaux $定义为一个tableaux家族，自然而然地由订单理想产生，并且显示出任何$λ$，几乎最小的形状$λ$的tableaux在不同的（弱）$ k $ k $ knuth等价类中。我们还讨论并在霍普金斯对坡度同源性的相关猜想上取得了一些进展。
Rowmotion is an invertible operator on the order ideals of a poset which has been extensively studied and is well understood for the rectangle poset. In this paper, we show that rowmotion is equivariant with respect to a bijection of Hamaker, Patrias, Pechenik and Williams between order ideals of rectangle and trapezoid posets, thereby affirming a conjecture of Hopkins that the rectangle and trapezoid posets have the same rowmotion orbit structures. Our main tools in proving this are $K$-jeu-de-taquin and (weak) $K$-Knuth equivalence of increasing tableaux. We define $almost$ $minimal$ $tableaux$ as a family of tableaux naturally arising from order ideals and show for any $λ$, the almost minimal tableaux of shape $λ$ are in different (weak) $K$-Knuth equivalence classes. We also discuss and make some progress on related conjectures of Hopkins on down-degree homomesy.
