论文标题
左切割和诱导的sidorenko bigraphs
Left-cut-percolation and induced-Sidorenko bigraphs
论文作者
论文摘要
Sidorenko Bigraph是一个在Bigraphon $ w $中的密度在$ W $恒定时的最小化。文献的几种技术证明了Sidorenko属性包括将（通常在树分解中）分解为具有更强特性的较小构件。这种突出的技术是conlon的$ n $ compositions-lee，它使用弱的Hölder（或弱规范）Bigraphs作为构件。反过来，为了获得弱的hölderbigraphs，通常使用含义的含义bigraph $ \ \ \ \ cut cut-cut-percolating bigraph $ \ theme是薄弱的hölderbigraph。在Razborov作者的较早结果中，我们提供了$ n $分解的概括，称为Reflective Tree Decompositions，这些分解使用了较弱的构建块，称为诱导的Sidorenko Bigraphs，还可以获得Sidorenko Bigraphs。 在本文中，我们表明了反射bigraph和剪切的bigraph概念的“左侧”版本产生了类似的含义链：左反射bigraph $ \暗示$左切 - 渗透bigraph $ \暗示$暗示$诱导的 - 诱导的sidorenko bigraph。我们还表明，在轻度假设下，可以使用弱的霍德特性的“左侧”类似物（也可以通过类似的含义链获得）来改善Conlon的另一个结果的界限-Lee- lee大致表明，大的bigraphs在每个实现程度的右侧具有足够的顶点，具有sidorenko属性。
A Sidorenko bigraph is one whose density in a bigraphon $W$ is minimized precisely when $W$ is constant. Several techniques of the literature to prove the Sidorenko property consist of decomposing (typically in a tree decomposition) the bigraph into smaller building blocks with stronger properties. One prominent such technique is that of $N$-decompositions of Conlon--Lee, which uses weakly Hölder (or weakly norming) bigraphs as building blocks. In turn, to obtain weakly Hölder bigraphs, it is typical to use the chain of implications reflection bigraph $\implies$ cut-percolating bigraph $\implies$ weakly Hölder bigraph. In an earlier result by the author with Razborov, we provided a generalization of $N$-decompositions, called reflective tree decompositions, that uses much weaker building blocks, called induced-Sidorenko bigraphs, to also obtain Sidorenko bigraphs. In this paper, we show that "left-sided" versions of the concepts of reflection bigraph and cut-percolating bigraph yield a similar chain of implications: left-reflection bigraph $\implies$ left-cut-percolating bigraph $\implies$ induced-Sidorenko bigraph. We also show that under mild hypotheses, the "left-sided" analogue of the weakly Hölder property (which is also obtained via a similar chain of implications) can be used to improve bounds on another result of Conlon--Lee that roughly says that bigraphs with enough vertices on the right side of each realized degree have the Sidorenko property.
