论文标题
3向$（V，K，2）$ Steiner Trade的频谱完成
A Completion of the spectrum of 3-way $(v,k,2)$ Steiner trades
论文作者
论文摘要
A 3向$（v，k，t）$交易$ t $ $ m $由三个成对的脱节集合$ t_1 $，$ t_2 $和$ t_3 $，每个$ m $ $ k $的$ m $块我\ leq 3 $。如果发现的任何$ t $ -subset（$ t $）最多一次在$ t_i $中以$ 1 \ leq i \ leq 3 $发生，则$ t $称为3-way $（v，k，k，t）$ steiner trade。我们试图通过应用一些块，bibds，rbs，rbs，gdds，rgdds和$ r \ times $ r \ times s $ taking网格块来完成频谱$ s_ {3s}（v，k）$，所有可能的体积尺寸的集合（V，v，v，k，2）$ steiner Trade。以前，我们获得了一些3向$（V，K，2）$ Steiner Trade的结果。特别是，我们证明存在一个3向$（v，k，2）$ steiner $ m $ $ m $时，$ 12（k-1）\ leq m $，价格为$ 15 \ leq k $（Rashidi and Soltankhah，2016年）。现在，我们证明该索赔也适用于$ k \ leq 14 $。
A 3-way $(v,k,t)$ trade $T$ of volume $m$ consists of three pairwise disjoint collections $T_1$, $T_2$ and $T_3$, each of $m$ blocks of size $k$, such that for every $t$-subset of $v$-set $V$, the number of blocks containing this $t$-subset is the same in each $T_i$ for $1\leq i\leq 3$. If any $t$-subset of found($T$) occurs at most once in each $T_i$ for $1\leq i\leq 3$, then $T$ is called 3-way $(v,k,t)$ Steiner trade. We attempt to complete the spectrum $S_{3s}(v,k)$, the set of all possible volume sizes, for 3-way $(v,k,2)$ Steiner trades, by applying some block designs, such as BIBDs, RBs, GDDs, RGDDs, and $r\times s$ packing grid blocks. Previously, we obtained some results about the existence some 3-way $(v,k,2)$ Steiner trades. In particular, we proved that there exists a 3-way $(v,k,2)$ Steiner trade of volume $m$ when $12(k-1)\leq m$ for $15\leq k$ (Rashidi and Soltankhah, 2016). Now, we show that the claim is correct also for $k\leq 14$.
