论文标题
晶格步行区组合，一些显着的三角款和类似Apéry的数字
Lattice walk area combinatorics, some remarkable trigonometric sums and Apéry-like numbers
论文作者
论文摘要
明确的代数区域枚举公式是为了概括规范的平方晶格步道的各种晶格步道，尤其是作者最近引入的三角晶格手性步行。枚举中的一个关键要素是衍生一些涉及三角分和的显着身份 - 这也是非琐碎量子模型（例如hofstadter模型）的重要组成部分 - 及其在多个二项式总和方面的显式重写。还通过数字理论和某些类似Apéry的数字，Apéry数字的表亲（2）和ζ（3）在非理性性考虑中起着核心作用的APéry数字的表兄弟（3），这是一种有趣的联系。
Explicit algebraic area enumeration formulae are derived for various lattice walks generalizing the canonical square lattice walk, and in particular for the triangular lattice chiral walk recently introduced by the authors. A key element in the enumeration is the derivation of some remarkable identities involving trigonometric sums --which are also important building blocks of non trivial quantum models such as the Hofstadter model-- and their explicit rewriting in terms of multiple binomial sums. An intriguing connection is also made with number theory and some classes of Apéry-like numbers, the cousins of the Apéry numbers which play a central role in irrationality considerations for ζ(2) and ζ(3).
