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Involutary pemutations over finite fields given by trinomials and quadrinomials
P Vanchinathan, Anitha G
For all finite fields of elements where we have constructed permutation polynomials which have order 2 as permutations, and have 3 terms, or 4 terms as polynom…
An Elementary Problem in Galois Theory about the Roots of Irreducible Polynomials
M Krithika, P Vanchinathan
For a field , and a root of an irreducible polynomial over (in some algebraic closure) the number of roots of lying in is studied here. Given such an $f(x)…
Collection of Polynomials over Finite Fields Providing Involutary Permutations
P Vanchinathan, Kevinsam B
For an odd prime power satisfying we construct totally permutation polyomials, all giving involutory permutations with exactly fi…
Exceptional Quartics are Ubiquitous
Aruna C, P Vanchinathan
For each real quadratic field we constructively show the existence of infinitely many exceptional quartic number fields containing that quadratic field. On the other hand, another…
Construction of Permutation Polynomials of Certain Specific Cycle Structure over Finite Fields
Anitha G, P Vanchinathan
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements bei…