A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it virtually nilpotent. However, until now the only examples known were abelian. In this note we furnish an example 2-step nilpotent having certain set.

Bootle et al. (EUROCRYPT 2016) construct an extremely efficient zero-knowledge argument for arithmetic circuit satisfiability in the discrete logarithm setting. However, the argument does not treat relations involving commitments, and furthermore, for simple polynomial relations, the complex machinery employed is unnecessary. In this work, we give a framework for expressing simple relations bet...

let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.

In this paper we derive the bi-orthogonality relations, diagonal term evaluations and evaluation formulas for the non-symmetric Koornwinder polynomials. For the derivation we use certain representations of the (double) affine Hecke algebra which were originally defined by Noumi and Sahi. We furthermore give the explicit connection between the non-symmetric and the symmetric theory. This leads i...

It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial F ∈ C[x] of degree n at n complex-valued points can be done with Õ(n) exact field operations in C, where Õ(·) means that we omit polylogarithmic factors. We complement this result by an analysis of approximate multipoint evaluation of F to a precision of L bits after the binary po...