标题： 多米诺骨牌铺砌，非交叉格路和Koutschan-Krattenthaler-Schlosser行列式的子类 显示英文标题

标题： Domino tilings, nonintersecting lattice paths and subclasses of Koutschan-Krattenthaler-Schlosser determinants

摘要： 库茨汉、克拉滕塔勒和施洛瑟最近考虑了一类二项式行列式。 在本工作中，我们给出了这些行列式的两个子类的组合解释，分别涉及多米诺骨牌铺砌和非交叉格点路径，从而部分回答了他们提出的问题。 此外，库茨汉、克拉滕塔勒和施洛瑟建立的行列式求值为我们的多米诺骨牌铺砌和非交叉格点路径的加权计数产生了许多乘积公式。 然而，仍有两个计数对应于这三人提出的猜想公式。 我们在此使用全纯Ansatz原理结合创造性的望远镜方法的模约简方法证明了这两个猜想，从而填补了这一空白。 显示英文摘要

摘要： Koutschan, Krattenthaler and Schlosser recently considered a family of binomial determinants. In this work, we give combinatorial interpretations of two subclasses of these determinants in terms of domino tilings and nonintersecting lattice paths, thereby partially answering a question of theirs. Furthermore, the determinant evaluations established by Koutschan, Krattenthaler and Schlosser produce many product formulas for our weighted enumerations of domino tilings and nonintersecting lattice paths. However, there are still two enumerations left corresponding to conjectural formulas made by the three. We hereby prove the two conjectures using the principle of holonomic Ansatz plus the approach of modular reduction for creative telescoping, and hence fill the gap.