Frobenius numbersgenusquadratic numbersApéry setIn this paper, we give closed-form expressions of the $p$-Frobenius number for the triple of the numbers $a n(n-1)+r$ for an integer $a\\ge 4$ and $r$ is odd. For the set of given positive integers $A:=\\{a_{1},a_{2},\\...
Therefore, the Frobenius norm of the incidence matrix can be expressed in terms of the number of edges in the graph, |E|, as E(G)F=2|E|. It follows that the DNDS H2-norm is only dependent on the number of edges in the graph rather than the actual structure of the topology. ...
On the one hand, we investigate the relation between the genus and the Frobenius number. On the other hand, for two fixed positive integers g1, g2, we give necessary and sufficient conditions in order to have a numerical semigroup S such that {g1, g2} is the set of its pseudo-...
Fabien Pazuki_ Bounds for the number of rational points on curves over global fi 53:58 Francesc Fité_ The generalized Sato-Tate conjecture 58:52 Andrzej Schinzel_ The Congruence f ( x ) g ( y ) c = 0 (mod xy ) 30:27 Borwein integrals 13:07 Francesc Fité_ Sato-Tate axioms...
In particular, a p-Frobenius integer number associated with an affine semigroup was introduced in Ref. [1]. In this work, for an affine semigroup S, we introduce the concept of p-Frobenius vector of S (with respect to a graded monomial order ), which is defined as F0(S) = max {C...
For d=2 one has a three-dimensional Frobenius manifold QH*(P2) with where Nk= number of rational curves on P2 passing through 3k−1 generic points. WDVV [5] yields (Kontsevich and Manin 1994) recursion relations for the numbers Nk starting from N1=1. The closed analytic formula for th...
An Euler pseudoprime to the base a is an odd composite number n with (a, n) = 1 such that a (n−1)/2 ≡ a n mod n. An Euler pseudoprime to the base a is also a pseudoprime to the base a. If n ≡ 1 mod 4, we can also look at a (n−1)/2 k for k > 1, and...
the generating functionΦ(d3;z) for the setΔ(d3). We find the Frobenius numberF(d3), the genusG(d3), and the Hilbert seriesH(d3;z) of a graded subring for nonsymmetric and symmetric semigroupsS(d3)and enhance the lower bounds ofF(d3) for symmetric and nonsymmetric semigroups...
Moreover, as a consequence, we are able to obtain the pseudo-Frobenius numbers of the 2-semigroups and 3-semigroups. In Sect. 4 we prove that, if l is an even number (odd number, respectively), then any l-semigroup with Frobenius number F can be obtained from a symmetric (pseudo...
To start off with, what are Frobenius numbers? First of all, we’ll attempt to visualize what exactly this problem states. Imagine that we have a number n of coins. These coins can be worth any natural number value, such as two, three,...