Pico Gilman

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math.CO2024

Congruence Classes of Simplex Structures in Finite Field Vector Spaces

Timothy Cheek, Joseph Cooper, Pico Gilman +6

We study a generalization of the Erdős-Falconer distance problem over finite fields. For a graph $G$ , two embeddings $p, p^{'} : V (G) \to F_{q}^{d}$ of a graph $G$ are congruent i…

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…