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On the Yeh-Bradley conjecture on linear trend-free block designs. (English) Zbl 0799.62084
Summary: C. M. Yeh and R. A. Bradley [Commun. Stat., Theory Methods 12, 1-24 (1983; Zbl 0523.62071)] conjectured that every binary connected block design with blocks of size $$k$$ and a constant replication number $$r$$ for each treatment can be converted to a linear trend-free design by permuting the positions of treaments within blocks if and only if $$r(k+1) \equiv 0 \pmod 2$$. This conjecture is studied. Results include: (i) the conjecture is true whenever the block size is even and (ii) the conjecture is true for BIB designs.

##### MSC:
 62K10 Statistical block designs 05B05 Combinatorial aspects of block designs
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