Mahonian数与对数凹性的类比

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2022-10-18 DOI:10.1007/s00026-022-00614-2

Yousra Ghemit, Moussa Ahmia

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引用次数: 0

摘要

在本文中，我们提出了长度为n的具有由Mahonian数已知的k个逆的置换数i（n，k）的q类似。我们研究了有用的性质和一些格路径/划分和tilings的组合解释。此外，我们分别给出了k和n中q-Mahonian数的强q-log腔的两个构造性证明。特别是对于（q=1\），我们分别得到了Mahonian数在k和n中的对数凹性的两个构造性证明。

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An Analogue of Mahonian Numbers and Log-Concavity

In this paper, we propose a q-analogue of the number of permutations i(n, k) of length n having k inversions known by Mahonian numbers. We investigate useful properties and some combinatorial interpretations by lattice paths/partitions and tilings. Furthermore, we give two constructive proofs of the strong q-log-concavity of the q-Mahonian numbers in k and n, respectively. In particular for \(q=1\), we obtain two constructive proofs of the log-concavity of the Mahonian numbers in k and n, respectively.

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来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches