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Maximal number of zeros in a row of the character table of the symmetric group S_n.
1

%I #7 Jul 17 2020 13:18:15

%S 0,0,1,2,4,7,9,16,19,34,39,55,75,113,153,199,245,318,426,499,733,866,

%T 1110,1347,1794,2099,2667,3559,4087,5219

%N Maximal number of zeros in a row of the character table of the symmetric group S_n.

%o Contribution from Chris Cummins (cummins(AT)mathstat.concordia.ca), Apr 16 2010: (Start)

%o (GAP) max:=25;

%o for n in [1..max] do

%o ir:=Irr(CharacterTable(SymmetricGroup(n)));

%o Print(Maximum(List(ir,m->Length(Filtered(List(m,IsZero),k->k=true)))));

%o if n<max then Print(", ");else Print("\n");fi;

%o od; (End)

%K nonn,more

%O 1,4

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 24 2003

%E More terms computed using GAP. Chris Cummins (cummins(AT)mathstat.concordia.ca), Apr 16 2010

%E a(26)-a(30) from _Alexander R. Miller_, Jul 16 2020