Glenn Bruda

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20242026

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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.CO2025

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.CO2025

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

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…