Asymptotic enumeration of sparse uniform hypergraphs with given degrees. (January 2016)

• Record Type: Journal Article
• Authors: Blinovsky, Vladimir; Greenhill, Catherine
• Is Part Of: European journal of combinatorics. Volume 51(2016:Jan.)
• Page Start: 287
• Page End: 296
• Publication Date: 2016-01
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2015.06.004
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: Let r ≥ 2 be a fixed integer. For infinitely many n, let k = ( k 1, …, k n ) be a vector of nonnegative integers such that their sum M is divisible by r . We present an asymptotic enumeration formula for simple 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 ( M ) .