Permutations with extremal number of fixed points
نویسندگان
چکیده
Abstract. We extend Stanley’s work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting permutations we study their generating polynomials by number of excedances. Several techniques are used: Désarménien’s desarrangement combinatorics, Gessel’s hookfactorization and the analytical properties of two new permutation statistics “DEZ” and “lec”. Explicit formulas for the maximal case are derived in terms of symmetric functions.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 116 شماره
صفحات -
تاریخ انتشار 2009