Related papers: Expected Frobenius numbers

We develop a finite-dimensional approximation of the Frobenius-Perron operator using the finite volume method applied to the continuity equation for the evolution of probability. A Courant-Friedrichs-Lewy condition ensures that the…

We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and…

We obtain a Fourier dimension estimate for sets of exact approximation order introduced by Bugeaud for certain approximation functions $\psi$. This Fourier dimension estimate implies that these sets of exact approximation order contain…

The famous linear diophantine problem of Frobenius is the problem to determine the largest integer (Frobenius number) whose number of representations in terms of $a_1,\dots,a_k$ is at most zero, that is not representable. In other words,…

For a finite partially ordered set we calculate the dimension of the variety of its subspace representations having fixed dimension vector. The dimension is given in terms of the Euler quadratic form associated with a partially ordered set,…

We determine the order of magnitude of the variance of the Fibonacci partition function. The answer is different to the most naive guess. The proof involves a diophantine system and an inhomogeneous linear recurrence.

A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. The size of its complement is called the genus and the largest number in the complement is called its Frobenius number. We consider the set of…

We propose a notion of Frobenius-Perron dimension for certain free $\mathbb{Z}$-modules of infinite rank and compute it for the $\mathbb{Z}$-modules of finite dimensional complex representations of unitary groups with nonnegative dominant…

In this paper an explicit formula for a lower bound on the volume of a hyperbolic orbifold, dependent on dimension and the maximal order of torsion in the orbifolds' fundamental group, is constructed.

We study parabolic bundles on an algebraic curve in positive characteristic. Our motivation is to properly formulate Frobenius pull-backs of parabolic bundles in a way that extends various previous facts and arguments for the usual…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

De Loera, O'Neill and Wilburne introduced a general model for random numerical semigroups in which each positive integer is chosen independently with some probability p to be a generator, and proved upper and lower bounds on the expected…

For positive integers $a$, $b$, and $c$ which have no common divisor, the Frobenius number of $a$, $b$ and $c$ is defined to be the largest integer that cannot be expressed as a linear combination of $a$, $b$ and $c$ with non-negative…

We consider a finite fields version of the Erd\H{o}s-Falconer distance problem for two different sets. In a certain range for the sizes of the two sets we obtain results of the conjectured order of magnitude.

We classify Frobenius forms, a special class of homogeneous polynomials in characteristic $p>0$, in up to five variables over an algebraically closed field. We also point out some of the similarities with quadratic forms.

Let K/Q be Galois, and let eta in K* whose conjugates are multiplicatively independent. For a prime p, unramified, prime to eta, let np be the residue degree of p and gp the number of P I p, then let o\_P(eta) and o\_p(eta) be the orders of…

Many results on the convex order in the literature were stated for random variables with finite mean. For instance, a fundamental result in dependence modeling is that the sum of a pair of random random variables is upper bounded in convex…

We consider the expected value of $\mbox{Tr}(\Theta_C^n)$ where $C$ runs over a thin family of $r$-cyclic covers of $\mathbb{P}^1_{\mathbb{F}_q}$ for any $r$. We obtain many lower order terms dependent on the divisors of $r$. We use these…

We construct blocks of finite groups with arbitrarily large $\mathcal{O}$-Morita Frobenius numbers. There are no known examples of two blocks defined over $\mathcal{O}$ that are not Morita equivalent but the corresponding blocks defined…

This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…