可分解的Hybrid三元系大集和超大集的构造

The Constructions for Large Sets and Overlarge Sets of Resolvable Hybrid Triple Systems

中文关键词:  Hybrid三元系  大集  超大集  平行类  几乎平行类

英文关键词:Hybrid triple system  large set  overlarge set  parallel class  almost parallel classes

中文摘要:

      一个 LRHTS$(v)$ (或 LARHTS$(v)$), 是指一个集合 $\{(X , {\cal B}_i):1\leq i \leq 4(v-2)\}$, 其中每个$(X, {\cal B }_i)$都构成一个可分解的(或几乎可分解的) HTS$(v)$, 并且所有的 ${\cal B}_i$ 构成 $X$中全部 循环和可迁三元组的分拆.一个 OLRHTS$(v)$ (或OLARHTS$(v)$), 是指一个族$\{(Y\backslash \{y\}, \A_y^j) : y\in Y, j=0, 1, 2, 3\}, $ 其中~$Y$为$v+1$ 元集, 对于每个~$y\in Y, j=0, 1, 2,3, ~(Y\backslash \{y\}, \A_y^j)$ 是一个可分解的(或几乎可分解的)HTS$(v)$, 并且所有 $\A_y^j$ 构成 $Y$中全部循环和可迁三元组的分拆.本文中, 我们应用直接构造和递归构造方法, 讨论了 LRHTS$(v)$,LARHTS$(v)$, OLRHTS$ $ $(v)$, OLARHTS$(v)$的存在性问题,得到了一些新的结果.

英文摘要:

      An LRHTS$(v)$~(or LARHTS$(v))$ is a collection of $\{(X , {\cal B }_i):1\leq i \leq 4(v-2)\}$, where $X$ is a $v$-set, each $(X, {\cal B}_i)$ is a resolvable $($or almost resolvable$)$ HTS$(v)$, and all ${\cal B}_i$s form a partition of all cycle triples and transitive triples on $X$. An OLRHTS$(v)~ ($or OLARHTS$(v))$ is a collection $\{(Y\backslash \{y\}, \A_y^j) : y\in Y, j=0, 1, 2, 3\}, $ where $Y$ is a $(v+1)$-set, each $(Y\backslash \{y\}, {\cal A}_y^j)$ is a resolvable $($or almost resolvable$)$ HTS$(v)$, and all ${\cal A}_y^j$s form a partition of all cycle and transitive triples on $Y$. In this paper, we establish some directed and recursive constructions for LRHTS$(v)$, LARHTS$(v)$, OLRHTS$(v)$, OLARHTS$(v)$ and give some new results.