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On the existence of $d$-homogeneous $3$-way Steiner trades | | H. Amjadi
; N. Soltankhah
; | | Date: |
29 Oct 2016 | | Abstract: | A $mu$-way $(v, k, t)$ trade $T = {T_{1} , T_{2}, . . ., T_{mu} }$ of
volume $m$ consists of $mu$ disjoint collections $T_{1}, T_{2}, ldots,
T_{mu}$, 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 $1 leq i leq mu$). A $mu$-way $(v, k, t)$ trade is called
$mu$-way $(v, k, t)$ Steiner trade if any $t$-subset of found$(T)$ occurs at
most once in $T_{1}$ $(T_{j}, j geq 2)$. A $mu$-way $(v,k,t)$ trade is
called $d$-homogeneous if each element of $V$ occurs in precisely $d$ blocks of
$T_{1}$ $(T_{j},~ j geq 2)$. In this paper we characterize the $3$-way
$3$-homogeneous $(v,3,2)$ Steiner trades of volume $v$. Also we show how to
construct a $3$-way $d$-homogeneous $(v,3,2)$ Steiner trade for $din
{4,5,6}$, except for seven small values of $v$. | | Source: | arXiv, 1610.9489 | | Services: | Forum | Review | PDF | Favorites | |
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