發(fā)布時(shí)間：2018-12-16 08:25

【摘要】：一個(gè)階數(shù)為v,指標(biāo)為λ的有向燭臺(tái)形t-設(shè)計(jì)DCSλ(t,K,v)是一個(gè)四元組(X,S,g,B),其中x是一個(gè)v元集；S是x的一個(gè)s元子集(稱(chēng)作干)；g是由x\S的一些非空子集構(gòu)成的集合(其元素稱(chēng)作組),且劃分X\S;召是X的某些有向子集構(gòu)成的集合(其元素稱(chēng)作區(qū)組),且對(duì)任意B∈B,有|B|∈K；并且x中任意一個(gè)有向t-子集T,如果對(duì)每個(gè)i,|T∩(S∪Gi)|t,那么T恰好包含于召的λ個(gè)區(qū)組中；而對(duì)任意i,S ∪ Gi的任意有向t-子集都不包含于召中任何區(qū)組中.若g有ni個(gè)大小為gi的組(1≤i≤r),并且干的大小為s,則記其型為(91n1 92n2…grnr:s)當(dāng)t=3,K={4}時(shí),常稱(chēng)其為指標(biāo)為λ的有向燭臺(tái)形四元系,記作DCQSλ(g1n1 g2n2…grnr:s).有向燭臺(tái)形設(shè)計(jì)是燭臺(tái)形設(shè)計(jì)的推廣形式.它在構(gòu)作有向t-設(shè)計(jì)時(shí)起重要作用.本文利用遞歸構(gòu)作與直接構(gòu)作相結(jié)合的方法討論了有向燭臺(tái)形四元系的存在性問(wèn)題,給出了如下一些結(jié)果：(1)DCQSλ(gn:0)存在的充要條件為λg(n-1)三0(mod 2),λgn≡0(mod 2),λg2n(n-1)[g(n+1)-3]≡0(mod 4),n≥3,g≥1.(2)DCQSλ(g2:0)存在的充要條件為λg≡0(mod 2),g≥2.(3)DCQSλ(g4:s)存在的充要條件為λg≡0(mod 2),λs≡0(mod 2),0≤s≤ 2g,g≥1.(4)當(dāng)λ,g,s滿(mǎn)足下列條件時(shí),存在DCQSλ(g3:s).(a)λ≡1(mod 2),g≡0(mod 2),s≡0(mod 2),0≤s≤g,g≥2;(b)λ≡0(mod 2),0≤s≤g,g≥1.(5)當(dāng)λ,g,s滿(mǎn)足下列條件時(shí),存在DCQSλ(g5:s).(a)λ≡1(mod 2),g≡0(mod 2),s≡0(mod 2),0≤s≤3g,g≥2;(b)λ≡0(mod 2),0≤s≤3g,g≥1.
[Abstract]:A directed candlestick t- design DCS 位 (tn Knv) with order v and index 位 is a quaternion (XG), where x is a set of v elements, S is a subset of s elements of x (called dry). G is a set composed of some nonempty subsets of x\ S (whose elements are called groups) and is divided into X\ S.The calling is a set of some directed subsets of X (whose elements are called block groups), and for any B 鈭，

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