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Bollobas, Bela
Few subsequence sums in Z_n x Z_n ★★
Conjecture For every
, the sequence in
consisting of
copes of
and
copies of
has the fewest number of distinct subsequence sums over all zero-free sequences from
of length
.
![$ 0 \le t \le n-1 $](/files/tex/3f439dde8bba9a34c4b73a7bf35d2ba2d600dd53.png)
![$ {\mathbb Z}_n^2 $](/files/tex/784102d74f41429c112d0dd6746a4ab9f1957afe.png)
![$ n-1 $](/files/tex/da6174078cbeae6601684c08526200d9254caa11.png)
![$ (1,0) $](/files/tex/02e6ed02ec9ede67b905b1ca3c64be3eb3c6f11b.png)
![$ t $](/files/tex/4761b031c89840e8cd2cda5b53fbc90c308530f3.png)
![$ (0,1) $](/files/tex/2f2f87361c58fc118cefb1ab5cb288a25e20007f.png)
![$ {\mathbb Z}_n^2 $](/files/tex/784102d74f41429c112d0dd6746a4ab9f1957afe.png)
![$ n-1+t $](/files/tex/26b23f9cc4119b690ed97ea8d21da62ec7899f64.png)
Keywords: subsequence sum; zero sum
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