The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences

Mehdi Omidali 1
  • 1 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran. Current address: Department of Mathematics, Bu-Ali Sina University, P. O. Box 65175-4161, Hamedan, Iran

Abstract.

Studying certain combinatorial properties of non-unique factorizations have been a subject of recent literature. Little is known about two combinatorial invariants, namely the catenary degree and the tame degree, even in the case of numerical monoids. In this paper we compute these invariants for a certain class of numerical monoids generated by generalized arithmetic sequences. We also show that the difference between the tame degree and the catenary degree can be arbitrary large even if the number of minimal generators is fixed.

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