A122916 Minimum number of n-candidate full-rank-order ballots required to instantiate any tournament on n nodes (where A beats B in the tournament if and only if it does so in a majority of the ballots and we forbid pairwise ties).

1, 3, 3, 3, 3

Offset

1,2

Comments

Every entry is an odd number. a(n) <= a(n+1) <= a(n)+4. For all large enough n we know Cn/log(n) < a(n) < Kn/log(n) for suitable constants 0<C<K. Additional entries should be within the reach of computers. a(19) >= 5.

Links

Table of n, a(n) for n=1..5.

P. Erdos and L. Moser, On the representation of directed graphs as unions of orderings, Publ. Math. Inst. Hungar. Acad. Sci. 9 (1964) 125-132; also reprinted in Paul Erdos: The art of counting, Selected writings (ed. Joel Spencer) MIT Press 1973, pp. 79-86.

Warren D. Smith, Answer to puzzle 28 (surveys the problem)

Richard Stearns, The voting problem, Amer. Math. Monthly 66 (1959) 761-763. Warning: Erdos, Moser and Stearns actually consider a slightly different problem definition, where ties are allowed. That would define a different sequence which would upper-bound this one and is related to it, but the present sequence seems to be a little more pleasant.

Crossrefs

Sequence in context: A333537 A227827 A033700 * A300372 A132973 A107760

Adjacent sequences: A122913 A122914 A122915 * A122917 A122918 A122919

Keyword

hard,more,nonn

Author

Warren D. Smith, Sep 19 2006

Status

approved