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On the possible volume of $mu$-$(v,k,t)$ trades | | Saeedeh Rashidi
; Nasrin Soltankhah
; | | Date: |
29 Oct 2013 | | Abstract: | A $mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $mu$ disjoint
collections $T_1$, $T_2, dots T_{mu}$, each of $m$ blocks, such that for
every $t$-subset of $v$-set $V$ the number of blocks containing this t-subset
is the same in each $T_i (1leq ileq mu)$. In other words any pair of
collections ${T_i,T_j}$, $1leq i<j leq mu$ is a $(v,k,t)$ trade of volume
$m$.
In this paper we investigate the existence of $mu$-way $(v,k,t)$ trades and
also we prove the existence of: (i)~3-way $(v,k,1)$ trades (Steiner trades) of
each volume $m,mgeq2$. (ii) 3-way $(v,k,2)$ trades of each volume $m,mgeq6$
except possibly $m=7$. We establish the non-existence of 3-way $(v,3,2)$ trade
of volume 7. It is shown that the volume of a 3-way $(v,k,2)$ Steiner trade is
at least $2k$ for $kgeq4$. Also the spectrum of 3-way $(v,k,2)$ Steiner trades
for $k=3$ and 4 are specified. | | Source: | arXiv, 1310.7759 | | Services: | Forum | Review | PDF | Favorites | |
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