pub fn burnside_ring_product(
degree: usize,
gens: &[Perm],
cap: usize,
) -> Option<Vec<Vec<Vec<i128>>>>Expand description
The Burnside ring multiplication of G = ⟨gens⟩ — the structure constants N[a][b][l] giving the
decomposition of the product G-set (G/H_a) × (G/H_b) = ⊔_l N[a][b][l]·(G/H_l) into transitive G-sets,
indexed by the conjugacy classes of subgroups (same order as table_of_marks).
Marks are multiplicative — a subgroup fixes a pair iff it fixes each coordinate — so the mark vector of a
product is the componentwise product of the factors’ mark vectors; the (triangular, invertible) table of
marks is then back-substituted to recover the multiplicities. This is the multiplication of the Burnside
ring, the G-set analogue of the tensor/fusion ring of the character table (tensor_decomposition).
FAIL-CLOSED: None if any back-substitution is inexact (it never is for genuine G-sets, so this
certifies the result). Coefficients are non-negative integers.