A study of permutation polynomials as Latin squares

Bhatta, Vadiraja G. R.; Shankar, B R

doi:10.1142/9789813207363_0025

Cited by 2 publications

(3 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Vadiraja and Shankar [27] motivated by the work of Rivest continued the study of permutation polynomials over the ring (Z n , +, •) by studying Latin squares represented by linear and quadratic bivariate polynomials over Z n when n = 2 w with the characterization of some PPs. Some of the main results they got are stated below.…”

Section: Mollin and Smallmentioning

confidence: 99%

See 1 more Smart Citation

Varieties of groupoids and quasigroups generated by linear-bivariate polynomials over ring Z_n

Ilojide,

Jaiyeola,

Owojori

2014

Preprint

View full text Add to dashboard Cite

Some varieties of groupoids and quasigroups generated by linear-bivariate polynomials P (x, y) = a + bx + cy over the ring Z n are studied. Necessary and sufficient conditions for such groupoids and quasigroups to obey identities which involve one, two, three (e.g. Bol-Moufang type) and four variables w.r.t. a, b and c are established. Necessary and sufficient conditions for such groupoids and quasigroups to obey some inverse properties w.r.t. a, b and c are also established. This class of groupoids and quasigroups are found to belong to some varieties of groupoids and quasigroups such as medial groupoid(quasigroup), F-quasigroup, semi automorphic inverse property groupoid(quasigroup) and automorphic inverse property groupoid(quasigroup).

show abstract

Section: Mollin and Smallmentioning

confidence: 99%

“…Furthermore, Vadiraja and Shankar [27] were able to find examples of pairs of orthogonal Latin squares generated by bivariate polynomials over Z n when n = 2 w which was found impossible by Rivest for bivariate polynomials over Z n when n = 2 w .…”

Section: Theorem 12 (Vadiraja and Shankar [27])mentioning

confidence: 99%

Varieties of groupoids and quasigroups generated by linear-bivariate polynomials over ring Z_n

Ilojide,

Jaiyeola,

Owojori

2014

Preprint

View full text Add to dashboard Cite

show abstract

“…So, in case of the rings Z n , we see that there are n m+1 polynomials of degree m. Some of them will be permutation polynomials depending both on n and coefficients. The structures and various properties of permutation polynomials are explained in detail in [19,3,4,20,2,14].…”

Section: Introductionmentioning

confidence: 99%