金藤特征多项式的二次系数

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED Annals of Combinatorics Pub Date : 2022-12-17 DOI:10.1007/s00026-022-00611-5

Mikołaj Marciniak

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引用次数: 2

摘要

Goulden–Rattan多项式根据描述Young图宏观形状的某些量\（（C_i）\）给出了对称群的归一化特征的子主导部分的精确值。Goulden–Rattan正猜想指出，这些多项式的系数是具有小分母的正有理数。通过应用某些涉及映射的双射（即在曲面上绘制的图），我们证明了二次项（C_2^2）的系数的这一猜想的一个特例。

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Quadratic Coefficients of Goulden–Rattan Character Polynomials

Goulden–Rattan polynomials give the exact value of the subdominant part of the normalized characters of the symmetric groups in terms of certain quantities \((C_i)\) which describe the macroscopic shape of the Young diagram. The Goulden–Rattan positivity conjecture states that the coefficients of these polynomials are positive rational numbers with small denominators. We prove a special case of this conjecture for the coefficient of the quadratic term \(C_2^2\) by applying certain bijections involving maps (i.e., graphs drawn on surfaces).

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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

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