推广poto nik和Šajna关于顶点传递自互补k-超图存在的条件

Pub Date : 2022-11-25 DOI:10.7151/dmgt.2360

L. Lesniak, Henri Thuiller, A. Wojda

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引用次数: 0

摘要

抽象Letℓ 是正整数，k=2ℓ 或k=2ℓ + 设n是一个正整数，其中n≠1（mod 2ℓ+1）。对于素数p，n（p）表示最大整数i，使得pi除n。Potočnik和Šajna证明了如果存在n阶的顶点传递自补k-超图，那么对于每个素数p，我们都有pn（p）lect 1（mod 2ℓ+1）。在这里，我们将它们的结果扩展到一个更大的整数类k。

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Extending Potočnik and Šajna’s Conditions on the Existence of Vertex-Transitive Self-Complementary k-Hypergraphs

Abstract Let ℓ be a positive integer, k = 2ℓ or k = 2ℓ + 1, and let n be a positive integer with n ≡ 1 (mod 2ℓ+1). For a prime p, n(p) denotes the largest integer i such that pi divides n. Potočnik and Šajna showed that if there exists a vertex-transitive self-complementary k-hypergraph of order n, then for every prime p we have pn(p) ≡ 1 (mod 2ℓ+1). Here we extend their result to a larger class of integers k.

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