Compton’s method of proving monadic second-order limit laws is based on analyzing the generating function of a class of finite structures. For applications of his deeper results we previously relied… (More)

We generalize a result of Bateman and Erdős concerning partitions, thereby answering a question of Compton. From this result it follows that if K is a class of finite relational structures that is… (More)

— We prove a quantitative version of a result of Furstenberg [20] and Deligne [13] stating that the the diagonal of a multivariate algebraic power series with coefficients in a field of positive… (More)

Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series T(z)… (More)

We study words on a finite alphabet avoiding a finite collection of patterns. Given a pattern p in which every letter that occurs in p occurs at least twice, we show that the number of words of… (More)

Given an affine domain of Gelfand–Kirillov dimension 2 over an algebraically closed field, it is shown that the centralizer of any non-scalar element of this domain is a commutative domain of… (More)

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… (More)

We consider real sequences (fn) that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where… (More)

Abstract. Dirichlet density extends global asymptotic density in an additive number system A whose generating series A(x) diverges at its radius of convergence (see [1], p. 50). This note shows that… (More)