Results on permutations with distinct difference property
DOI:
https://doi.org/10.11575/cdm.v4i1.61878Abstract
We prove that for all odd primes $p$ and positive integers $\alpha \geq 2$, a construction of Batten and Sane yields at least $(p-1)^3/4$ permutations with a distinct difference property (DDP) of $\{1,2,\ldots,p^\alpha-1\}$. 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.Downloads
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