Pelikán's conjecture and cyclotomic cosets

F. J. MacWilliams, A. M. Odlyzko

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)110-114
Number of pages5
JournalJournal of Combinatorial Theory, Series A
Issue number1
StatePublished - Jan 1977
Externally publishedYes


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