Dr. Cai Yue from the School of Information Management of JUFE published, as the first author, a paper titled Vector Parking Functions with Periodic Boundaries and Rational Parking Functions in the Journal of Combinatorial Theory, Series A, an international SCI journal in combinatorial mathematics. The abstract: Vector parking functions are sequences of non-negative integers whose order statistics are bounded by a given integer sequence. Using the theory of fractional power series and an analog of Newton-Puiseux Theorem, the paper derives the exponential generating function for the number of u-parking functions when u is periodic. The method is to convert an Appell relation of Gončarov polynomials to a system of linear equations. Solving the system, Dr. Cai obtains an explicit formula of the exponential generating function in terms of Schur functions of certain fractional power series. In particular, the authors apply their methods to rational parking functions for which the boundary is induced by a linear function with rational slope.
The Journal of Combinatorial Theory, Series A, published by Elsevier, one of the world's largest publishers of scientific and technological literature, is a top international journal in the field of combinatorial mathematics.