Inversion polynomials for 321-avoiding permutations
نویسندگان
چکیده
We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formulas for the major index polynomial of 321-avoiding permutations. Other properties of these polynomials are investigated as well. Our tools include Dyck and 2-Motzkin paths, polyominoes, and continued fractions.
منابع مشابه
Inversion polynomials for 321-avoiding permutations: addendum
This addendum contains results about the inversion number and major index polynomials for permutations avoiding 321 which did not fit well into the original paper. In particular, we consider symmetry, unimodality, behavior modulo 2, and signed enumeration.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 313 شماره
صفحات -
تاریخ انتشار 2013