With China’s educational reform, college physical education teaching mode has also made some innovations. Sports club is a new modern education model developed on the basis of traditional physical education courses. It provides students with more choices and is convenient for autonomous learning, thus forming a student-centered engineering education model. With the background of sports reform, this paper investigates and analyzes the reform of sports club system in universities, puts forward specific implementation means to stimulate the development process of sports reform in universities in China, puts forward data analysis schemes, and analyzes and guides the reform of sports club system. The specific research results show that our reform plan has been recognized by 92% of students and 94% of teachers.

Paths that consist of up-steps of one unit and down-steps of \(k\) units, being bounded below by a horizontal line \(-t\), behave like \(t+1\) ordered tuples of \(k\)-Dyck paths, provided that \(t\le k\). We describe the general case, allowing \(t\) also to be larger. Arguments are bijective and/or analytic.