Two-generator numerical semigroups and Fermat and Marsenne numbers
Résumé
Given $g\in \N$, what is the number of numerical semigroups $S=\vs{a,b}$ in $\N$ of genus $|\N\setminus S|=g$? After settling the case $g=2^k$ for all $k$, we show that attempting to extend the result to $g=p^k$ for all odd primes $p$ is linked, quite surprisingly, to the factorization of Fermat and Mersenne numbers.
Domaines
Combinatoire [math.CO]Origine | Fichiers produits par l'(les) auteur(s) |
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