奇异辫子
Singular Meanders
AI总结：
本文研究了允许曲线切线交点的广义辫子，建立组合框架并列举了若干自然家族。
摘要：
辫子计数问题自四十年前提出以来仍未解决。最近发现辫子可分解为素因子，这引出更广泛的对象——奇异辫子，允许曲线切线交点。本文系统研究了奇异辫子，发展了基本组合框架，指出了与其他组合对象和已知整数序列的联系，并完全列举了若干自然家族的奇异辫子。
英文摘要：
The problem of enumerating meanders -- pairs of simple plane curves with transverse intersections -- was formulated about forty years ago and is still far from solved. Recently, it was discovered that meanders admit a factorization into prime components. This factorization naturally leads to a broader class of objects, which we call singular meanders, in which tangential intersections between the curves are also allowed. In the present paper we initiate a systematic study of singular meanders: we develop a basic combinatorial framework, point out connections with other combinatorial objects and known integer sequences, and completely enumerate several natural families of singular meanders.
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。
