A363701 Numbers k with the property that the character table of S_k contains a zero in every nontrivial column.

0, 1, 5, 6, 8, 9, 10, 12, 14, 17, 21, 28, 30, 32, 34, 36, 37

Offset: 1

Author

Diego Martin Duro, Jun 16 2023

Keywords

• nonn
• more
• hard

Comments

This sequence contains A363675 and A363676.

Crossrefs

Cf. A000217, A010054, A175595, A260682, A363675, A363676.

Programs

Sage

def zeros(n):
    G = SymmetricGroup(n)
    N = G.character_table()
    for j in range(1,N.ncols()):
        if 0 not in N[:,j]:
            return False
        j+=1
    return True
n=1
while n>0:
    if zeros(n) == True:
        print(n)
    n+=1