Let n > 1 be an integer, and let Fp denote a field of p elements for a prime p ≡ 1 (mod n). By 2015, the question of existence or nonexistence of n-th power residue difference sets in Fp had been settled for all n < 24. We settle the case n = 24 by proving the nonexistence of 24-th power residue difference sets in Fp. We also prove the nonexistence of qualified 24-th power residue difference se...

An algorithm for detecting intrinsically knotted graphs, yielding many new minor minimal IK graphs. Ramin Naimi Occidental College We describe an algorithm that detects seemingly most (and possibly all) intrinsically knotted (IK) graphs, and can help find knotless embeddings for graphs that are not IK. We have used this algorithm, implemented as a Mathematica program, to find many new minor min...

We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function FC of three variables. E-mail: [email protected] E-mail: kniehl@de...

Symbolic computation in algebraic categories provides computer implementations for modern algebra theories. The present paper reveals the utility of the parameterized categorical approach by deriving a multivariate polynomial category (over various coefficient domains), which is used by our Mathematica implementation of Buchberger’s algorithms for determining the Gröbner basis. These implementa...