A274332 Team size n for which there exists a balanced tournament for 2n+1 players so that in 2n+1 matches each player plays exactly n-1 times with and n times against each other player.

1, 2, 3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, 23, 26, 29, 30, 33

Offset

0,2

Comments

There are 2n+1 players and 2n+1 matches. In each match one person rests, and the remaining 2n players are divided into two equal teams.

Up to n=33 there is probably only a unique design (up to permutation), and it has point / mirror symmetry.

It is conjectured that this sequence is identical to A005097 (ref. Kohen link).

a(n) = A130290(n+2) = A102781(n+2) = A139791(n+1) = A005097(n+1) for 0 <= n <= 17. - Georg Fischer, Oct 30 2018

Links

Table of n, a(n) for n=0..17.

Daniel Kohen and Ivan Sadofschi, A New Approach on the Seating Couples Problem, arXiv:1006.2571 [math.CO], 2010.

Formula

Conjectured design scheme for Team 1 (N:= 2n+1; here players count from 0..2n): X, X+1 (mod N), X+1+2 (mod N), X+1+2+3 (mod N), ...; X = 0..2n (match number). Resting player: (X + (n*(n+1)/2) (mod N).

Example

n=5:
Match 1: 1,2,3,5,8 versus 4,7,9,10,11
Match 2: 2,3,4,6,9 versus 5,8,10,11,1
Matches 3..11: further cyclic permutations

Crossrefs

Cf. A005097, A102781, A130290, A139791.

Sequence in context: A097702 A347912 A082583 * A005097 A102781 A130290

Adjacent sequences: A274329 A274330 A274331 * A274333 A274334 A274335

Keyword

nonn,more

Author

Michael Steyer, Jun 22 2016

Status

approved