Glenn Bruda

activity

20222026

collaborators

11 papers

math.NT2026

On digit-appending walks along linear recurrences

Arya Mosahab, Sahitya Boyyakar, Glenn Bruda +2

We study digit-appending walks in base $b \geq 2$ along integer linear recurrences with minimal characteristic polynomials having a unique simple dominant root $α$ that lies outside…

math.CO2026

Enumerating binary words restricted by subsequence frequency

Glenn Bruda

Let $p$ be a binary word of length $ℓ$ with $r \geq 2$ runs. Previously known only for $k \leq 4$ , we show for $n$ sufficiently large that the number of binary words of length $n$ w…

math.NT2026

Generalized polygonal number representations

Glenn Bruda

Let $r_{n}^{k} (N)$ be the number of representations of $N$ as the sum of $n$ generalized $k$ -gonal numbers and $r_{n}^{□} (N)$ be the number of representations of $N$ as the sum o…

math.PR2025

The Limiting Spectral Distribution of Various Matrix Ensembles Under the Anticommutator Operation

Glenn Bruda, Bruce Fang, Raul Marquez +6

Inspired by the quantization of classical quantities and Rankin Selberg convolution, we study the anticommutator operation ${\cdot, \cdot}$ , where ${A, B} = A B + B A$ , applied to…

math.CO2024

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals

Glenn Bruda

Defining a family of recurrences, we generalize Comtet's formula for the generating function of the enumeration of indecomposable permutations. Consequently, we generalize Panaitop…

math.MG2024

Gromov-Hausdorff distances between quotient metric spaces

Henry Adams, Armando Albornoz, Glenn Bruda +7

The Hausdorff distance measures how far apart two sets are in a common metric space. By contrast, the Gromov-Hausdorff distance provides a notion of distance between two abstract m…

math.GM2024

An alternative proof of the Puiseux representation of the exponential integral

Glenn Bruda

Working from definitions and an elementarily obtained integral formula for the Euler-Mascheroni constant, we give an alternative proof of the classical Puiseux representation of th…

math.CO2024

A closed formula for linear recurrences with constant coefficients

Glenn Bruda, Bruce Fang, Pico Gilman +6

Given a linear recurrence of the form $c_{n} = a_{1} c_{n - 1} + \dots + a_{j} c_{n - j}$ , it is well-known that $c_{n} = \sum_{r} p_{r} (n) r^{n}$ , where the sum is taken over the set of characteristic root…

math.CO2024

Variants of Conway Checkers and k-nacci Jumping

Glenn Bruda, Joseph Cooper, Kareem Jaber +2

Conway Checkers is a game played with a checker placed in each square of the lower half of an infinite checkerboard. Pieces move by jumping over an adjacent checker, removing the c…

math.CV2024

On the convergence of Newton series and the asymptotics of finite differences

Glenn Bruda

Suppose a complex function $f$ has a Lebesgue measurable inverse Laplace transform. We show that the $n$ th order forward and backward differences of $f$ at $z_{0} \in C$ tend…

math.GM2022

Maclaurin Integration: A Weapon Against Infamous Integrals

Glenn Bruda

Maclaurin Integration is a new series-based technique for solving infamously difficult integrals in terms of elementary functions. It has fairly liberal conditions for sound use, m…