John Fairfax-Ball

collaborators

4 papers

math.NT2026

Sharp $p$ -adic Extrema and Least Extremal Rows for Restricted Binomial GCDs

John Fairfax-Ball

For integers $m \geq 2$ and rows $N > m$ divisible by $m$ , consider the restricted binomial greatest common divisor $G (N; m) = g cd {(k N) : 0 < k < N, m ∣ k}$ . Fix a prime $p$ with $p\…

math.CO2026

A Fixed-Offset Transition for Random Stackability on Paths

John Fairfax-Ball

We study a support-collapse version of graph pebbling on paths. A configuration is stackable if a sequence of legal pebbling moves can produce a nonzero configuration supported on…

math.NT2026

Restricted Binomial GCDs at Primes Congruent to -1

John Fairfax-Ball

For integers $m \geq 2$ and $m ∣ N$ , let $G (N; m) = g cd {(k N) : 0 < k < N, m ∣ k}$ . We prove a complete $p$ -adic valuation formula for $G (N; m)$ at primes $p \equiv - 1 (mod m)$ ,…

math.CO2026

The stacking number of a tree

John Fairfax-Ball

The stacking number of a graph is the least integer t >= 2 such that every configuration of t pebbles can be transformed by pebbling moves into a configuration supported on one ver…

Sharp p-adic Extrema and Least Extremal Rows for Restricted Binomial GCDs

A Fixed-Offset Transition for Random Stackability on Paths

Restricted Binomial GCDs at Primes Congruent to -1

The stacking number of a tree

Sharp $p$ -adic Extrema and Least Extremal Rows for Restricted Binomial GCDs