Proving a conjecture about distinct difference property in permutations, suggesting further research questions.
We prove that for all odd primes p and positive integers α≥2, a construction of Batten and Sane yields at least (p−1)3 /4 permutations with a distinct difference property (DDP) of {1,2,…,pα−1}. This proves a conjecture of Batten and Sane, that at least (p−1)2/2 such permutations exist. We also pose several research questions for DDP permutations.
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Bell et al. (2009) studied this question.
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