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- Title
CANTOR POLYNOMIALS FOR SEMIGROUP SECTORS.
- Authors
NATHANSON, MELVYN B.
- Abstract
A packing function on a set Ω in Rn is a one-to-one correspondence between the set of lattice points in Ω and the set N0 of non-negative integers. It is proved that if r and s are relatively prime positive integers such that r divides s - 1, then there exist two distinct quadratic packing polynomials on the sector {(x, y) ∈ R2 : 0 ≤ y ≤ rx/s}. For the rational numbers 1/s, these are the unique quadratic packing polynomials. Moreover, quadratic quasi-polynomial packing functions are constructed for all rational sectors.
- Subjects
CANTOR distribution; POLYNOMIALS; SEMIGROUPS (Algebra); LATTICE theory; GROUP theory; INTEGERS; QUADRATIC equations
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 5, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S021949881350165X