论文标题
通过流程多面体的两种简单产物的子分区代数
A subdivision algebra for a product of two simplices via flow polytopes
论文作者
论文摘要
对于晶格路径$ν$从原点到点$（a，b）$使用步骤$ e =（1,0）$和$ n =（0,1）$，我们构造了一个关联的流polytope $ \ nathcal {f} _ {\ hat {ghat {g hat {g} _b（g} _b（n）_b（n n n n）} $从acycycelection poper wre bidirectional wre biDiRiDiriDiriDirectional wrecectional biDiRectional。我们表明，流polytope $ \ mathcal {f} _ {\ hat {g} _b（ν）} $接纳了$ w $ -simplex的细分双dual，其中$ w $是路径$ \ barbarν=eνn$中的v $ w $。可以通过减少允许负根部的无环根多型的梅萨罗斯（Mészáros）分区代数的多项式$p_ν$来获得此细分的改进。通过$ \ MATHCAL {f} _ {\ hat {g} _b（ν）} $与简单的产物$Δ_A\ timesδ_b$之间的整体等价性，我们从而为两个简单的产品获得了一个细分代数。作为一种特殊情况，我们给出了减少$P_ν$的减少订单，该$P_ν$产生了Ceballos，Padrol和Sarmiento的环状$ν$ -Tamari Complex。
For a lattice path $ν$ from the origin to a point $(a,b)$ using steps $E=(1,0)$ and $N=(0,1)$, we construct an associated flow polytope $\mathcal{F}_{\hat{G}_B(ν)}$ arising from an acyclic graph where bidirectional edges are permitted. We show that the flow polytope $\mathcal{F}_{\hat{G}_B(ν)}$ admits a subdivision dual to a $w$-simplex, where $w$ is the number of valleys in the path $\barν = EνN$. Refinements of this subdivision can be obtained by reductions of a polynomial $P_ν$ in a generalization of Mészáros' subdivision algebra for acyclic root polytopes where negative roots are allowed. Via an integral equivalence between $\mathcal{F}_{\hat{G}_B(ν)}$ and the product of simplices $Δ_a\times Δ_b$, we thereby obtain a subdivision algebra for a product of two simplices. As a special case, we give a reduction order for reducing $P_ν$ that yields the cyclic $ν$-Tamari complex of Ceballos, Padrol, and Sarmiento.
