From the 1 of 7 linked papers with an AI index.
7 papers
Small Matrices with Large Inverses: Unimodular Cases
Steven Finch
The paper investigates how close a 4×4 unimodular matrix can be to singularity, analyzing ternary and non‑negative cases as the entry range expands.
Small Matrices with Small Inverses: Unimodular Zerofree Cases
Steven Finch
We consider unimodular matrices such that neither nor contain zero entries. Matrices typically exhibit a trade-off: small imply large . We investigate…
th Roots of th Powers
Steven Finch
Seeking simple, efficient solutions of a matrix equation leads (quite circuitously) to optimizing unimodular zerofree matrices. Canonicalizing such matrices under signed-permutatio…
Popa's "Recurrent Sequences" and Reciprocity
Steven Finch
Dumitru Popa found asymptotic expansions for certain nonlinear recurrences, but left open the numerical evaluation of associated constants. We address this issue. A change of varia…
A Deceptively Simple Quadratic Recurrence
Steven Finch
Standard techniques for treating linear recurrences no longer apply for quadratic recurrences. It is not hard to determine asymptotics for a specific parametrized model over a wide…
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.