The difference between consecutive members of a difference set $(\textrm {mod}$ $v)$
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- Proc. Amer. Math. Soc. 46 (1974), 150-154 Request permission
Abstract:
Let $\mathcal {D} = \{ {d_1},{d_2}, \cdots ,{d_k}\}$ be a difference set $\pmod v$ so that for any $d\not \equiv 0\pmod v$ there are exactly $\lambda$ pairs $({d_i},{d_j}),{d_i},{d_j}\in \mathcal {D}$ such that ${d_i} - {d_j} \equiv d\pmod v$. Suppose further that $0 \leq {d_1} < {d_2} < \cdots < {d_k} < v$ and write ${d_{k + 1}} = v+ {d_1}$. The following two results are proved: (i) $\Sigma _{i = 1}^k{({d_{i + 1}} - {d_i})^2} = O(({v^2}/k)\log k),$ (ii) ${\max _{1 \leqslant i \leqslant k}}({d_{i + 1}} - {d_i}) = O(v/\surd k).$References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 150-154
- MSC: Primary 05B10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0345843-2
- MathSciNet review: 0345843