The Eulerian distribution on involutions is indeed unimodal
نویسندگان
چکیده
منابع مشابه
5 The Eulerian Distribution on Involutions is Indeed Unimodal
A sequence a0, a1, . . . , an of real numbers is said to be unimodal if for some 0 ≤ j ≤ n we have a0 ≤ a1 ≤ · · · ≤ aj ≥ aj+1 ≥ · · · ≥ an, and is said to be log-concave if a 2 i ≥ ai−1ai+1 for all 1 ≤ i ≤ n − 1. Clearly a log-concave sequence of positive terms is unimodal. The reader is referred to Stanley’s survey [10] for the surprisingly rich variety of methods to show that a sequence is l...
متن کاملThe Eulerian distribution on involutions is indeed unimodal
Let In,k (respectively, Jn,k) be the number of involutions (respectively, fixed-point free involutions) of {1, . . . , n} with k descents. Motivated by Brenti’s conjecture which states that the sequence In,0, In,1, . . . , In,n−1 is log-concave, we prove that the two sequences In,k and J2n,k are unimodal in k, for all n. Furthermore, we conjecture that there are nonnegative integers an,k such t...
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A sequence a0, a1, . . . , an of real numbers is said to be unimodal if for some 0 ≤ j ≤ n we have a0 ≤ a1 ≤ · · · ≤ aj ≥ aj+1 ≥ · · · ≥ an, and is said to be log-concave if a 2 i ≥ ai−1ai+1 for all 1 ≤ i ≤ n − 1. Clearly a log-concave sequence of positive terms is unimodal. The reader is referred to Stanley’s survey [10] for the surprisingly rich variety of methods to show that a sequence is l...
متن کاملThe Eulerian distribution on centrosymmetric involutions
We present an extensive study of the Eulerian distribution on the set of centrosymmetric involutions, namely, involutions in Sn satisfying the property σ(i) + σ(n+ 1− i) = n+ 1 for every i = 1 . . . n. We find some combinatorial properties for the generating polynomial of such distribution, together with an explicit formula for its coefficients. Afterwards, we carry out an analogous study for t...
متن کاملThe Eulerian distribution on self evacuated involutions
We present an extensive study of the Eulerian distribution on the set of self evacuated involutions, namely, involutions corresponding to standard Young tableaux that are fixed under the Schützenberger map. We find some combinatorial properties for the generating polynomial of such distribution, together with an explicit formula for its coefficients. Afterwards, we carry out an analogous study ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2006
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2005.10.002