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A new construction for µ-way Steiner trades | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 13، دوره 9، شماره 2، شهریور 2024، صفحه 329-338 اصل مقاله (393.53 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.27862.1373 | ||
| نویسندگان | ||
| Saeedeh Rashidi* 1؛ Nasrin Soltankhah2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Department of Mathematics, Faculty of mathematical Sciences, Alzahra University, Tehran, Iran | ||
| چکیده | ||
| A $\mu$-way $(v,k,t)$ trade $T$ of volume $m$ consists of $\mu$ pairwise disjoint collections $T_1, \ldots ,T_{\mu}$, each of $m$ blocks of size $k$ such that for every $t$-subset of a $v$-set $V,$ the number of blocks containing this $t$-subset is the same in each $T_i$ for $1\leq i\leq \mu$. If any $t$-subset of the $v$-set $V$ occurs at most once in each $T_i$ for $1\leq i\leq \mu$, then $T$ is called a $\mu$-way $(v,k,t)$ Steiner trade. In 2016, it was proved that there exists a 3-way $(v,k,2)$ Steiner trade of volume $m$ when $12(k-1)\leq m$ for each $k$. Here we improve the lower bound to $8(k-1)$ for even $k$, by using a recursive construction. | ||
| کلیدواژه‌ها | ||
| 3-way $(v, k, 2)$ Steiner trade؛ 1-solely balanced set؛ block design | ||
| مراجع | ||
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