Steven J. Miller

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20242026

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4 papers · 1 filter

math.CO2026

Braess' Paradox in Uniform Affine Grid Networks

Andy Lu, Steven J. Miller

Braess' Paradox is the phenomenon in which adding an edge to a congestion network increases total travel time. We study the paradox in directed rectangular grids where every edge s…

math.CO2024

Hyper-bishops, Hyper-rooks, and Hyper-queens: Percentage of Safe Squares on Higher Dimensional Chess Boards

Caroline Cashman, Joseph Cooper, Raul Marquez +2

The $n$ queens problem considers the maximum number of safe squares on an $n \times n$ chess board when placing $n$ queens; the answer is only known for small $n$ . Miller, Sheng an…

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…