OPAC (Online Public Access Catalog)
Pencarian Koleksi UPA Perpustakaan
start it by typing one or more keywords for title, author or subject
On numerical experiments with symmetric semigroup generated by three elements and their generalization
FEL, Leonid G - Personal Name
We give a simple explanation of numerical experiments of V. Arnold with two sequences of symmetric numerical semigroups, S(4, 6+4k, 87−4k) and S(9, 3+9k, 85−9k) generated by three elements. We present
generalization of these sequences by numerical semigroups S(r2 1 ,r1r2 + r2 1 k,r3 − r2 1 k), k ∈ Z, r1,r2,r3 ∈ Z+, r1 ≥ 2 and gcd(r1,r2) = gcd(r1,r3) = 1, and calculate their universal Frobenius number Φ(r1,r2,r3) for the wide range of k providing semigroups be symmetric. We show that this type of semigroups admit also nonsymmetric representatives. We describe the reduction of the minimal generating sets of these semigroups up to {r2 1 ,r3 − r2 1 k} for sporadic values of k and find these values by solving the quadratic Diophantine equation.
generalization of these sequences by numerical semigroups S(r2 1 ,r1r2 + r2 1 k,r3 − r2 1 k), k ∈ Z, r1,r2,r3 ∈ Z+, r1 ≥ 2 and gcd(r1,r2) = gcd(r1,r3) = 1, and calculate their universal Frobenius number Φ(r1,r2,r3) for the wide range of k providing semigroups be symmetric. We show that this type of semigroups admit also nonsymmetric representatives. We describe the reduction of the minimal generating sets of these semigroups up to {r2 1 ,r3 − r2 1 k} for sporadic values of k and find these values by solving the quadratic Diophantine equation.
Availability
| EB00000003416K | Available |
Detail Information
Series Title
-
Call Number
-
Publisher
: ,
Collation
-
Language
ISBN/ISSN
-
Classification
NONE
Detail Information
Content Type
E-Jurnal
Media Type
-
Carrier Type
-
Edition
-
Specific Detail Info
-
Statement of Responsibility
Leonid G. Fel
No other version available
File Attachment
