可分解的Hybrid三元系大集和超大集的构造

An LRHTS(v)(or LARHTS(v)) is a collection of {(X, B i) : 1 ≤ i ≤ 4(v-2)},where X is a v-set, each(X, B i) is a resolvable(or almost resolvable) HTS(v), and all 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 \{y}, A j y) : y ∈ Y, j = 0, 1, 2, 3}, where Y is a(v + 1)-set, each(Y \{y}, A j y)is a resolvable(or almost resolvable) HTS(v), and all A j y 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.

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

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.