Skip to Main content Skip to Navigation
Journal articles

On additive combinatorics of permutations of ℤn

Abstract : Let ℤn denote the ring of integers modulo n. A permutation of ℤn is a sequence of n distinct elements of ℤn. Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of ℤn, namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutation, and the maximum size of a collection of permutations such that no sum of two distinct permutations in the collection is a permutation. Let the sizes be denoted by s(n) and t(n) respectively. The case when n is even is trivial in both the cases, with s(n)=1 and t(n)=n!. For n odd, we prove (nφ(n))/2k≤s(n)≤n!· 2-(n-1)/2((n-1)/2)! and 2(n-1)/2·(n-1 / 2)!≤t(n)≤ 2k·(n-1)!/φ(n), where k is the number of distinct prime divisors of n and φ is the Euler's totient function.
Complete list of metadata

Cited literature [4 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185614
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 5:13:45 PM
Last modification on : Saturday, August 11, 2018 - 11:22:01 AM
Long-term archiving on: : Wednesday, April 26, 2017 - 10:09:57 AM

File

dmtcs-16-2-3.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01185614, version 1

Collections

Citation

L. Sunil Chandran, Deepak Rajendraprasad, Nitin Singh. On additive combinatorics of permutations of ℤn. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 2 (in progress) (2), pp.35--40. ⟨hal-01185614⟩

Share

Metrics

Record views

213

Files downloads

1138