Additive Latin transversals

Noga Alon

doi:10.1007/BF02773567

Additive Latin transversals

Noga Alon

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

We prove that for every odd prime p, every k ≤ p and every two subsets A = {a₁, . . . , a_k} and B = {b₁, . . . , b_k} of cardinality k each of Z_p, there is a permutation π ∈ S_k such that the sums a_i + b_π(i) (in Z_p) are pair-wise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related results as well.

Original language	English (US)
Pages (from-to)	125-130
Number of pages	6
Journal	Israel Journal of Mathematics
Volume	117
DOIs	https://doi.org/10.1007/BF02773567
State	Published - 2000
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF02773567

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title = "Additive Latin transversals",

abstract = "We prove that for every odd prime p, every k ≤ p and every two subsets A = {a1, . . . , ak} and B = {b1, . . . , bk} of cardinality k each of Zp, there is a permutation π ∈ Sk such that the sums ai + bπ(i) (in Zp) are pair-wise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related results as well.",

author = "Noga Alon",

year = "2000",

doi = "10.1007/BF02773567",

language = "English (US)",

volume = "117",

pages = "125--130",

journal = "Israel Journal of Mathematics",

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publisher = "Springer New York",

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T1 - Additive Latin transversals

AU - Alon, Noga

PY - 2000

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N2 - We prove that for every odd prime p, every k ≤ p and every two subsets A = {a1, . . . , ak} and B = {b1, . . . , bk} of cardinality k each of Zp, there is a permutation π ∈ Sk such that the sums ai + bπ(i) (in Zp) are pair-wise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related results as well.

AB - We prove that for every odd prime p, every k ≤ p and every two subsets A = {a1, . . . , ak} and B = {b1, . . . , bk} of cardinality k each of Zp, there is a permutation π ∈ Sk such that the sums ai + bπ(i) (in Zp) are pair-wise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related results as well.

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U2 - 10.1007/BF02773567

DO - 10.1007/BF02773567

M3 - Article

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SP - 125

EP - 130

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Additive Latin transversals

Abstract

All Science Journal Classification (ASJC) codes

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