Pelikán's conjecture and cyclotomic cosets

F. J. MacWilliams; A. M. Odlyzko

doi:10.1016/0097-3165(77)90070-X

Pelikán's conjecture and cyclotomic cosets

F. J. MacWilliams, A. M. Odlyzko

Mathematics

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

2 Scopus citations

Abstract

The following conjecture was recently made by J. Pelikán. Let a₀,..., a_n be an (n + 1)-tuple of 0's and 1's; let A_k = ε{lunate}_i=0^n-ka_ia_i+k for k = 0,..., n. Then if n ≥ 4 some A_k is even. This paper shows that Pelikán's conjecture is false for infinitely many values of n. On the other hand it is also shown that the conjecture is true for most values of n, and a characterization is given of those values of n for which it fails.

Original language	English (US)
Pages (from-to)	110-114
Number of pages	5
Journal	Journal of Combinatorial Theory, Series A
Volume	22
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(77)90070-X
State	Published - Jan 1977

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title = "Pelik{\'a}n's conjecture and cyclotomic cosets",

abstract = "The following conjecture was recently made by J. Pelik{\'a}n. Let a0,..., an be an (n + 1)-tuple of 0's and 1's; let Ak = ε{lunate}i=0n-kaiai+k for k = 0,..., n. Then if n ≥ 4 some Ak is even. This paper shows that Pelik{\'a}n's conjecture is false for infinitely many values of n. On the other hand it is also shown that the conjecture is true for most values of n, and a characterization is given of those values of n for which it fails.",

author = "MacWilliams, {F. J.} and Odlyzko, {A. M.}",

year = "1977",

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T1 - Pelikán's conjecture and cyclotomic cosets

AU - MacWilliams, F. J.

AU - Odlyzko, A. M.

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N2 - The following conjecture was recently made by J. Pelikán. Let a0,..., an be an (n + 1)-tuple of 0's and 1's; let Ak = ε{lunate}i=0n-kaiai+k for k = 0,..., n. Then if n ≥ 4 some Ak is even. This paper shows that Pelikán's conjecture is false for infinitely many values of n. On the other hand it is also shown that the conjecture is true for most values of n, and a characterization is given of those values of n for which it fails.

AB - The following conjecture was recently made by J. Pelikán. Let a0,..., an be an (n + 1)-tuple of 0's and 1's; let Ak = ε{lunate}i=0n-kaiai+k for k = 0,..., n. Then if n ≥ 4 some Ak is even. This paper shows that Pelikán's conjecture is false for infinitely many values of n. On the other hand it is also shown that the conjecture is true for most values of n, and a characterization is given of those values of n for which it fails.

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