Related papers: On the counting function for numerical monoids
We develop notions of integrable functions within the theory of schemic motivic integration.
As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular $k$-gons. For $n\le 4$ we determine formulas for the number $a_k(n)$ of generalized polyominoes consisting of $n$ regular $k$-gons.…
New estimates on the maximal function associated to the linear Schrodinger equation are established
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…
An approximate formula for complex Riemann Xi function, previously developed, is used to refine Backlund's estimate of the number of zeros till a chosen imaginary coordinate
We give an elementary characterization of rational functions among meromorphic functions in the complex plane.
We show that for every finite nonempty set L of integers greater than or equal to 2 there are a numerical monoid H and a squarefree element a $\in$ H whose set of lengths L(a) is equal to L.
In this note we define a generalization of Hall-Littlewood symmetric functions using formal group law and give an elementary proof of the generating function formula for the generalized Hall-Littlewood symmetric functions. We also give some…
We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
We introduce a "Hamiltonian"-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the…
The main purpose of this work is to prove characterization theorems for generalized moment functions on groups. According one of the main results these are exponential polynomials that can be described with the aid of complete (exponential)…
An observation on Hall-Littlewood polynomials.
We describe briefly in this note a procedure for consistently estimating the marginal likelihood of a statistical model through a sample from the posterior distribution of the model parameters.
Consider the representation of a rational number in the form, associated with "centered" Euclidean algorithm. We prove a new formula for the limit distribution function for sequences of rationals with bounded sum of partial quotients.
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
We prove that each counting function of the m-simple branched covers with a fixed genus of an elliptic curve is expressed as a polynomial of the Eisenstein series E_2, E_4 and E_6 . The special case m=2 is considered by Dijkgraaf.
In a paper entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent…
A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.