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Journal Articles SIAM Journal on Discrete Mathematics Year : 2011

Two-generator numerical semigroups and Fermat and Marsenne numbers

Abstract

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.
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Dates and versions

hal-00812743 , version 1 (22-04-2013)

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Shalom Eliahou, Jorge Ramirez Alfonsin. Two-generator numerical semigroups and Fermat and Marsenne numbers. SIAM Journal on Discrete Mathematics, 2011, 25, pp.622-630. ⟨10.1137/100787283⟩. ⟨hal-00812743⟩
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