منابع مشابه
On Fixed Points of Permutations
The number of fixed points of a random permutation of {1, 2, . . . , n} has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting attention to primitive actions, a complete classification of the limiting distributions is given. For most examples, they are trivial – almost every permutation has no fixed points. For the usual actio...
متن کاملPermutations with extremal number of fixed points
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, Ge...
متن کاملFixed Points and Excedances in Restricted Permutations
In this paper we prove that among the permutations of length n with i fixed points and j excedances, the number of 321-avoiding ones equals the number of 132-avoiding ones, for all given i, j ≤ n. We use a new technique involving diagonals of non-rational generating functions. This theorem generalizes a recent result of Robertson, Saracino and Zeilberger, for which we also give another, more di...
متن کاملThe largest and the smallest fixed points of permutations
We give a new interpretation of the derangement numbers dn as the sum of the values of the largest fixed points of all non-derangements of length n− 1. We also show that the analogous sum for the smallest fixed points equals the number of permutations of length n with at least two fixed points. We provide analytic and bijective proofs of both results, as well as a new recurrence for the derange...
متن کاملUnseparated pairs and fixed points in random permutations
Article history: Received 25 August 2013 Accepted 1 May 2014 Available online xxxx MSC: 60C05 60B15 60F05
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2008
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-008-0135-2