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arXiv · 0811.3758

Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

Vladimir L. Shchur
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Abstract

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit.

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Vladimir L. Shchur. 2009-02-13. Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3. https://doi.org/10.1007/s11853-010-0038-3

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