模式回避投票路径与有限算子演算
Pattern Avoiding Ballot Paths and Finite Operator Calculus
摘要：
避免选票路径的计数模式始于对模式的仔细分析。不是长度，而是模式的特征导致了难以找到明确的解决方案。某些特征，如右步和上步的重叠和差异，决定了递推公式的解。如果递归可以通过多项式序列来求解，则我们应用有限算子演算来找到关于二项式系数的解的显式形式。关键词：模式避免，投票路径，Dyck路径，有限算子演算，Umbral演算
英文摘要：
Counting pattern avoiding ballot paths begins with a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of right and up steps determine the solution of the recursion formula. If the recursion can be solved by a polynomial sequence, we apply the Finite Operator Calculus to find an explicit form of the solution in terms of binomial coefficients. Keywords: Pattern avoidance, ballot path, Dyck path, Finite Operator Calculus, Umbral Calculus
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
