  For a numerical semigroup S $\subseteq$ N with embedding dimension e,
conductor c and left part L = S $\cap$ [0, c -- 1], set W (S) = e|L| -- c. In
1978 Wilf asked, in equivalent terms, whether W (S) $\ge$ 0 always holds, a
question known since as Wilf's conjecture. Using a closely related lower bound
W 0 (S) $\le$ W (S), we show that if |L| $\le$ 12 then W 0 (S) $\ge$ 0, thereby
settling Wilf's conjecture in this case. This is best possible, since cases are
known where |L| = 13 and W 0 (S) = --1. Wilf's conjecture remains open for |L|
$\ge$ 13.

Combinatorics;Group Theory