Asymptotic enumeration of sparse uniform hypergraphs with given degrees

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• 作者：Vladimir Blinovsky^a ; ^b ; ^{vblinovs@yandex.ru" class="auth_mail" title="E-mail the corresponding author} ; Catherine Greenhill^c ; ^{c.greenhill@unsw.edu.au" class="auth_mail" title="E-mail the corresponding author}
• 刊名：European Journal of Combinatorics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：51
• 期：Complete
• 页码：287-296
• 全文大小：402 K

文摘

Let r≥2$r\ge 2$ be a fixed integer. For infinitely many n$n$, let $k=(k_1,\dots ,k_n)$ be a vector of nonnegative integers such that their sum M$M$ is divisible by r$r$. We present an asymptotic enumeration formula for simple r$r$-uniform hypergraphs with degree sequence $k$. (Here “simple” means that all edges are distinct and no edge contains a repeated vertex.) Our formula holds whenever the maximum degree $k_{\max }$ satisfies $k_{\max }^3=o\left(M\right)$.