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

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

2008-11-23

arxiv.org/abs/0811.3758v2

Funct. Anal. Other Math., 3 (2010) 97-101

Mathematics

Number Theory

Scientific paper

10.1007/s11853-010-0038-3

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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