| Summary: | 碩士 === 國立屏東大學 === 應用數學系碩士班 === 107 === We consider the bivariate polynomials of the 231-avoiding permutations with respect to major index and descent number, and make use a method of Dokos, Dwyer, johnson, Sagan, Selsor to prove a recurrence relation for the polynomials. We also consider the polynomials of the 231-avoiding permutations with respect to inversion number and the number of right-to-left minima. Then we use two methods to prove a recurrence relation for the polynomials in terms of Dyck paths and binary trees, respectively. Finally, we discuss a bijection between 231-avoiding permutations and Dyck path established by Stump, and Petersen’s description and the connection of the statistics mentioned above.
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