A Combinatorial Proof of the Log-Concavity of a Famous Sequence Counting Permutations

Author:

Bóna Miklós

Abstract

We provide a combinatorial proof for the fact that for any fixed $n$, the sequence $\{i(n,k)\}_{0\leq k\leq {n\choose 2}}$ of the numbers of permutations of length $n$ having $k$ inversions is log-concave.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. An Analogue of Mahonian Numbers and Log-Concavity;Annals of Combinatorics;2022-10-18

2. Formation of a giant component in the intersection graph of a random chord diagram;Journal of Combinatorial Theory, Series B;2017-07

3. Mean and Insensitive. Random Permutations;Combinatorics of Permutations;2016-04-19

4. On the connected components of a random permutation graph with a given number of edges;Journal of Combinatorial Theory, Series A;2013-11

5. Symmetry and Log-Concavity Results for Statistics on Fibonacci Tableaux;Annals of Combinatorics;2013-08-18

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