chess tournaments:

[Wouter Meeussen]

if it helps anyone, the 5, 16 and 59 scores for 3, 4 and 5 players are:

{{0,2,4},{0,3,3},{1,1,4},{1,2,3},{2,2,2}}

{{0,2,4,6},{0,2,5,5},{0,3,3,6},{0,3,4,5},{0,4,4,4},{1,1,4,6},{1,1,5,5},{1,2,3,
    6},{1,2,4,5},{1,3,3,5},{1,3,4,4},{2,2,2,6},{2,2,3,5},{2,2,4,4},{2,3,3,4},{
    3,3,3,3}}

{{0,2,4,6,8},{0,2,4,7,7},{0,2,5,5,8},{0,2,5,6,7},{0,2,6,6,6},{0,3,3,6,8},{0,3,
    3,7,7},{0,3,4,5,8},{0,3,4,6,7},{0,3,5,5,7},{0,3,5,6,6},{0,4,4,4,8},{0,4,4,
    5,7},{0,4,4,6,6},{0,4,5,5,6},{0,5,5,5,5},{1,1,4,6,8},{1,1,4,7,7},{1,1,5,5,
    8},{1,1,5,6,7},{1,1,6,6,6},{1,2,3,6,8},{1,2,3,7,7},{1,2,4,5,8},{1,2,4,6,
    7},{1,2,5,5,7},{1,2,5,6,6},{1,3,3,5,8},{1,3,3,6,7},{1,3,4,4,8},{1,3,4,5,
    7},{1,3,4,6,6},{1,3,5,5,6},{1,4,4,4,7},{1,4,4,5,6},{1,4,5,5,5},{2,2,2,6,
    8},{2,2,2,7,7},{2,2,3,5,8},{2,2,3,6,7},{2,2,4,4,8},{2,2,4,5,7},{2,2,4,6,
    6},{2,2,5,5,6},{2,3,3,4,8},{2,3,3,5,7},{2,3,3,6,6},{2,3,4,4,7},{2,3,4,5,
    6},{2,3,5,5,5},{2,4,4,4,6},{2,4,4,5,5},{3,3,3,3,8},{3,3,3,4,7},{3,3,3,5,
    6},{3,3,4,4,6},{3,3,4,5,5},{3,4,4,4,5},{4,4,4,4,4}}



At 11:32 23-04-99 -0400, N. J. A. Sloane wrote:
>
>%I A047657
>%S A047657 1,2,5,16,59,247
>%N A047657 Number of score sequences in chess tournament with n players
(with 3 outcomes for each game).
>%D A047657 P. A. MacMahon, Chess tournamemts and the like treated by the
calculus of symmetric functions, Coll. P
>apers I, MIT Press, 344-375.
>%O A047657 0,3
>%K A047657 nonn,more,nice
>%A A047657 njas
>%Y A047657 This is probably the same as either A028333 or A007747.
>%e A047657 With 3 players the possible scores are 420, 411, 330, 321, 222.
>
>This is probably the same as either A028333 or A007747, maybe someone could
check! 
>It is not obvious from the descriptions.
>Perhaps simplest thing would be if someone extended this sequence
>
>MacMahon also discusses the case of tournaments where there
>are n players and in each of the C(n,2) games one player gets
>3,2,1 or 0 points and the other player gets 0,1,2 or 3.
>How many different score sequences are there?
>This begins 1, 2, 8, 37 - more terms, someone?
>
>For 3 players the possible scores are
>630 621 540 531 522 441 432 333
>
>NJAs
>
>
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc at vandemoortele.be
eu000949 at pophost.eunet.be