A074025 Numbers k such that a triplewhist tournament TWh(k) exists.

1, 4, 8, 16

Offset: 1

Author

N. J. A. Sloane, Oct 16 2003

Keywords

• nonn
• more
• bref
• nice

Comments

The present state of knowledge, quoting from Ge (2007), is that a TWh(k) exists iff k == 0 or 1 (mod 4), except for k = 5, 9, 12, 13 and possibly 17.

After 16, the sequence continues 17?, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57, ...

Links

• G. Ge and C. W. H. Lam, Some new triplewhist tournaments TWh(v), J. Combinat. Theory, A101 (2003), 153-159.
• Gennian Ge, Triplewhist tournaments with the three person property, J. Combinat. Theory, A114 (2007), 1438-1455.
• Harri Haanpää and Petteri Kaski, The near resolvable 2-(13,4,3) designs and thirteen-player whist tournaments [shows that no TWh(13) exists]

Extensions

Of course this entry is much too short. But I have included it in the hope that this will encourage someone to settle the question of whether a(5) is 17 or 20 - i.e., does a TWh(17) exist?

Link supplied by Jon E. Schoenfield, Aug 01 2006

Edited by Andrey Zabolotskiy, Jan 17 2024