The Skolem-Mahler-Lech theorem states that if f(n) is a sequence given by a linear recurrence over a field of characteristic 0, then the set of m such that f(m) is equal to 0 is the union of a finite number of arithmetic progressions in m ≥ 0 and a finite set. We prove that if X is a subvariety of an affine variety Y over a field of characteristic 0 and q is a point in Y , and σ is an automorph...

Lech proved in 1953 that the set of zeroes of a linear recurrence sequence in a field of characteristic 0 is the union of a finite set and finitely many infinite arithmetic progressions. This result is known as the Skolem-Mahler-Lech theorem. Lech gave a counterexample to a similar statement in positive characteristic. We will present some more pathological examples. We will state and prove a c...

The Skolem–Mahler–Lech theorem states that if f(n) is a sequence given by a linear recurrence over a field of characteristic 0, then the set of m such that f(m) is equal to 0 is the union of a finite number of arithmetic progressions in m 0 and a finite set. We prove that if X is a subvariety of an affine variety Y over a field of characteristic 0 and q is a point in Y , and σ is an automorphis...

Motivated by the famous Skolem-Mahler-Lech theorem we initiate in this paper the study of a natural class of determinantal varieties, which we call Vandermonde varieties. They are closely related to the varieties consisting of all linear recurrence relations of a given order possessing a non-trivial solution vanishing at a given set of integers. In the regular case, i.e., when the dimension of ...

Let G be a graph with its vertices and edges. On defining bijective function ρ:V(G) →{0,1,...,p}. For each edge assign the label 1 if ρ*(ab)= | ρ(a) 2 −ρ(b) /ρ(a)−ρ(b) is odd or 0 otherwise such that |eρ(1) − eρ(0)| ≤ then labeling called as divided square difference cordial graph. We prove in this paper for relatively possible set of spider graphs atmost one legs greater than namely J(SP(1 m ,...