Related papers: On the counting function for numerical monoids
Morse matchings capture the essential structural information of discrete Morse functions. We show that computing optimal Morse matchings is NP-hard and give an integer programming formulation for the problem. Then we present polyhedral…
This paper presents a new methodology to count the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius…
We consider various counting questions for irreducible binomials over finite fields. We use various results from analytic number theory to investigate these questions.
We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…
The main aim of the paper is to present a general version of the Fourier Tauberian theorem for monotone functions. This result, together with Berezin's inequality, allows us to obtain a refined version the Li-Yau estimate for the counting…
A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…
In this paper, we propose a numerical method of Fourier transform based on hyperfunction theory. In the proposed method, we compute analytic functions called the defining functions, which give the desired Fourier transform as a…
We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.
We present closed forms for several functions that are fundamental in number theory and we explain the method used to obtain them. Concretely, we find formulas for the p-adic valuation, the number-of-divisors function, the sum-of-divisors…
We give estimates from below for the greatest prime factor of the n-th term of a binary recurrence sequence.
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
Estimates of some integrals related to variations of smooth functions are presented.
In this short note, we show that the number of monogenic submonoids of the full transformation monoid of degree $n$ for $n > 0$, equals the sum of the number of cyclic subgroups of the symmetric groups on $1$ to $n$ points. We also prove an…
Definition of the number of prime numbers in the given interval
A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid $S$, consider the family of "shifted" monoids $M_n$ obtained by adding $n$ to each generator of $S$. In this paper, we characterize the…
In this article we derive some polynomial inequalities for Mertens functions.
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.
We construct a version of kneading theory for families of monotonous functions on the real line. The generality of the setup covers two classical results from Milnor-Thurston's kneading theory: the first one is to dynamically characterise…
Computations in the cohomology of finite groups.
In this note, we consider the monoid $\mathcal{PIM}_{n}$ of all partial monotone transformations on a chain with $n$ elements whose domains and ranges are intervals and its submonoid $\mathcal{IM}_{n}$ constituted by the full…