Turán numbers and switching

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-07 DOI:10.1016/j.disc.2024.114275

Karen Gunderson , Jason Semeraro

引用次数: 0

Abstract

Using a switching operation on tournaments we obtain some new lower bounds on the Turán number of the r-graph on

r + 1

vertices with 3 edges. For

r = 4

, extremal examples were constructed using Paley tournaments in previous work. We show that these examples are unique (in a particular sense) using Fourier analysis.

A 3-tournament is a ‘higher order’ version of a tournament given by an alternating function on triples of distinct vertices in a vertex set. We show that 3-tournaments also enjoy a switching operation and use this to give a formula for the size of a switching class in terms of level permutations, generalising a result of Babai–Cameron.

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图兰数字和转换

利用锦标赛的切换操作，我们获得了 r+1 个顶点上有 3 条边的 r 图的图兰数的一些新下限。对于 r=4，我们在之前的工作中利用帕利锦标赛构建了极值实例。我们利用傅立叶分析法证明这些例子是唯一的（在特定意义上）。3-锦标赛是锦标赛的 "高阶 "版本，由顶点集合中不同顶点的三元组上的交替函数给出。我们证明了 3 锦标也有切换操作，并利用这一点给出了以水平排列为单位的切换类大小公式，从而推广了巴拜-卡梅隆的一个结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.