Functions and polynomials ($mod p^n$)

Bernstein's polynomials for convex functions and related results

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.

New semifields, PN and APN functions

Pseudofinite counting functions mod n

An Euler characteristic χ is definable if for every definable function f : X → Y and every r ∈ R, the set {y ∈ Y : χ(f−1(y)) = r} is definable. If R = Z/nZ and M is a finite structure, there is a (unique) Euler characteristic χ : Def(M) → Z/nZ assigning every set its size mod n. This χ is always strong and ∅definable. If M is an ultraproduct of finite structures, then there is a canonical stron...

Tutte polynomials of wheels via generating functions

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

Computing All MOD-Functions Simultaneously

The fundamental symmetric functions are EXk (equal to 1 if the sum of n input bits is exactly k), THk (the sum is at least k), and MODm,r (the sum is congruent to r modulo m). It is well known that all these functions and in fact any symmetric Boolean function have linear circuit size. Simple counting shows that the circuit complexity of computing n symmetric functions is Ω(n2−o(1)) for almost ...