单纯Handcuffed三元系的嵌入

Embeddings of Pure Handcuffed Triple Systems

本文证明了对任意给定的正整数λ，当且仅当λ（ｖ－１）≡λｖ（ｖ－１）≡λ（ｕ－１）≡λｕ（ｕ－１）≡（ｍｏｄ４），ｕ≥２ｖ＋１且λ２（ｖ－２）／３时，任一单纯Ｈａｎｄｃｕｆｆｅｄ三元系ＮＨ（ｖ，３，λ）可嵌入于某个单纯Ｈａｎｄｃｕｆｆｅｄ三元系ＮＨ（ｕ，３，λ）

It is proved in this paper that for arbitrary positive number A, a pure Handcuffed triple system NH(v, 3, λ) can be embedded in a pure Handcuffed triple system NH (u, 3, λ) if and only if A(v- 1 )≡λv(v- 1 ) ≡λ(u - 1 )≡λu(u - 1 )≡0 (mod 4), u≥2v+ 1, λ≤2 (v- 2 ) /3.