Related papers: On the critical exponent of generalized Thue-Morse…
The Hankel determinants of certain automatic sequences $f$ are evaluated, based on a calculation modulo a prime number. In most cases, the Hankel determinants of automatic sequences do not have any closed-form expressions; the traditional…
Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when…
We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for…
We consider the set of $n\times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matrices of a given rank and then apply them to count such…
The method of self-similar root approximants has earlier been shown to provide accurate interpolating formulas for functions for which small-variable expansions are given and the behaviour of the functions at large variables is known. Now…
The multiplicity Tutte polynomial, which includes the arithmetic Tutte polynomial, is a generalization of the classical Tutte polynomial of matroids. In this paper, we obtain an expression of the general coefficient and the expressions of…
We study the 'critical moments' of subcritical Gaussian multiplicative chaos (GMCs) in dimensions $d \leq 2$. In particular, we establish a fully explicit formula for the leading order asymptotics, which is closely related to large…
We show that the 2-abelian complexity of the infinite Thue-Morse word is 2-regular, and other properties of the 2-abelian complexity, most notably that it is a concatenation of palindromes of increasing length. We also show sharp bounds for…
The purpose of this paper is to introduce basic concepts that are fundamental in the examination of composite moduli, while avoiding the notoriously difficult problem of prime-factorization. We introduce a new class of numbers, called…
In this paper, we consider representations of integers as sums of generalized heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such…
This note is an attempt to attack a conjecture of Fraenkel and Simpson stated in 1998 concerning the number of distinct squares in a finite word. By counting the number of (right-)special factors, we give an upper bound of the number of…
Critical phenomena in globally coupled excitable elements are studied by focusing on a saddle-node bifurcation at the collective level. Critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation…
In this paper we study sums of Dirichlet series whose coefficients are terms of the Thue-Morse sequence and variations thereof. We find closed-form expressions for such sums in terms of known constants and functions including the Riemann…
We apply the Thom-Milnor theorem to obtain the upper bounds on the amount of isolated (1) critical points of a potential generated by several fixed point charges(Maxwell's problem on point charges), (2) critical points of SINR, (3) critical…
In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a series of positive rational terms is a transcendental number.…
When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.
We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the…
Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several…
In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a sum, product and quotient of some series of positive rational…
We construct, for the free group acting on its Cayley tree, boomerang subgroups whose critical exponent is arbitrarily close to the critical exponent of a given finitely generated subgroup.