A363676 -id:A363676 - cp's OEIS frontend

A363675 Numbers k such that the least common multiple of the degrees of the irreducible characters of S_k equals |S_k| = k!.

0, 1, 6, 10, 21, 36, 66, 105, 120, 136, 190, 210, 276, 325, 465, 496, 561, 630, 666, 741, 780, 990, 1081, 1176, 1225, 1540, 1596, 1830, 2080, 2145, 2346, 2556, 2926, 3081, 3160, 3240, 3486, 3570, 3916, 4005, 4186, 4560, 4656, 4950, 5050, 5356, 5460, 5886, 6105

Offset: 1

Diego Martin Duro, Jun 14 2023

nonn

Intersection of the sequences of numbers k such that there exists a 2-core partition of k (A267137) and a 3-core partition of k (A000217).

Alois P. Heinz, Table of n, a(n) for n = 1..100
Diego Martin Duro, Arithmetic Properties of Character Degrees and the Generalised Knutson Index, arXiv:2306.12408 [math.RT], 2023.

Cf. A000142, A000217, A010054, A033687, A175595, A260682, A267137, A363676, A363701.

From Alois P. Heinz, Jun 16 2023: (Start)
{ k : A175595(k,2) > 0 and A175595(k,3) > 0 }.
{ k : A010054(k) > 0 and A033687(k) > 0 }. (End)

More terms from Alois P. Heinz, Jun 16 2023

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

Original entry on oeis.org

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

Offset: 1

Diego Martin Duro, Jun 16 2023

This sequence contains A363675 and A363676.

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

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

cp's OEIS Frontend

A363675 Numbers k such that the least common multiple of the degrees of the irreducible characters of S_k equals |S_k| = k!.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions