平坦排列多项式的梯形性
Trapezoidality of flat arrangement polynomials
AI总结：
该研究证明了满维平坦向量排列对应的平坦排列多项式系数具有梯形性，解答了相关公开问题，还将该结果应用于连通欧拉图的穆拉苏吉-斯托伊梅诺夫多项式，得到其系数也具梯形性。
AI中文摘要：
福克斯猜想预测，交错纽结的亚历山大多项式系数的绝对值构成梯形序列。卡尔曼、梅萨罗斯和波斯托科夫利用与平坦向量排列相关的多项式，给出了特殊交错纽结梯形性的新证明。我们证明，对每个满维平坦向量排列，平坦排列多项式的系数均具有梯形性，解答了对应的公开问题。我们的证明从凸多面体的角度给出了该多项式的几何解释。作为应用，我们证明了每个连通欧拉图的穆拉苏吉-斯托伊梅诺夫多项式的系数均具有梯形性。
英文摘要：
Fox's conjecture predicts that the absolute values of the coefficients of the Alexander polynomial of an alternating link form a trapezoidal sequence. Kálmán, Mészáros, and Postnikov gave a new proof of trapezoidality for special alternating links using a polynomial associated with flat vector arrangements. We prove that the flat arrangement polynomial has trapezoidal coefficients for every full-dimensional flat vector arrangement, answering the corresponding open question. Our proof gives a geometric interpretation of this polynomial in terms of convex polytopes. As an application, we prove that the Murasugi--Stoimenow polynomial of every connected Eulerian digraph has trapezoidal coefficients.
