Steven Finch

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math.CO2026

Small Matrices with Large Inverses: Unimodular $4 \times 4$ Cases

Steven Finch

How close to singularity can an $n \times n$ unimodular matrix be? For ternary cases as $n$ increases, exact expressions are unlikely, but upon fixing $n = 4$ and assessing $(2 k + 1)$ -…

math.CO2026

Small Matrices with Small Inverses: Unimodular Zerofree Cases

Steven Finch

We consider unimodular matrices $M$ such that neither $M$ nor $M^{- 1}$ contain zero entries. Matrices typically exhibit a trade-off: small $M$ imply large $M^{- 1}$ . We investigate…

math.CO2024

An Exceptional Convolutional Recurrence

Steven Finch

A quadratic recurrence of Faltung type, arising via ancestral path lengths of random binary trees, turns out to be related to the Painlevé I differential equation.

math.CO2024

Multisum Sets

Steven Finch

Complete infinite multisum sets are eventually linear. After 30 years of sitting in a file cabinet, the proof (thanks to James H. Schmerl) is brought from darkness into light.

Small Matrices with Large Inverses: Unimodular 4×4 Cases

Small Matrices with Small Inverses: Unimodular Zerofree Cases

An Exceptional Convolutional Recurrence

Multisum Sets

Small Matrices with Large Inverses: Unimodular $4 \times 4$ Cases