4 papers
math.CO2026
The Tropical Algebra of Binary-Tree Height
Grant Molnar
The binary-tree height recursion defines an algebra on , with join given by and product \[ a\star b=\max\{a,b\}+1. \] We show that w…
math.GM2026
The Gregory function and its completed Gregory transform
Grant Molnar
We study the entire interpolation \[ \mathcal{G}(z)=\int_0^1 \binom{x}{z}\,dx \] of the Gregory coefficients. Its completion satisfies the positive Markov-transform identity \[ \fr…
math.HO2026
Integral-Differential Calculus
Grant Molnar
We give an exposition of the Newton-Leibniz calculus. We begin by defining the integral as a limit of Riemann sums, verify the integrals of the standard catalog of functions by dir…
stat.OT2026
On the symmetry of evidential support
Grant Molnar
For events and , we have \[ \mathbb{P}(A\mid B) > \mathbb{P}(A\mid \neg B) \qquad\Longleftrightarrow\qquad \mathbb{P}(B\mid A) > \mathbb{P}(B\mid \neg A) \] whenever all fou…