Marco Mantovanelli

collaborators

Showing math.COShow all

4 papers · 1 filter

math.CO2026

Averaged Extensions of Golomb's Triangular Recursion: Critical Invariance and Supercritical Constraints

Marco Mantovanelli

For an integer $m \geq 1$ and a parameter $α > 0$ , consider the nested recursion $$ Q_{α,m}(n)=1+\left\lfloor \fracα{m}\sum_{j=1}^m Q_{α,m}\!\left(n-Q_{α,m}(n-j)\right)\right\rfloor, \…

math.CO2026

Certified Return-Word Induction for a Perturbed Hofstadter Recursion

Marco Mantovanelli

We study the parity-perturbed Hofstadter recursion $Q (1) = Q (2) = 1, Q (n) = Q (n - Q (n - 1)) + Q (n - Q (n - 2)) + (- 1)^{n} .$ We prove that it is well-defined for every $n \geq 1$ by a computer-a…

math.CO2026

Quadratic Reduction and Classical Multiple-Index Fibonacci-Lucas Identities

Marco Mantovanelli

We place several classical identities in a common algebraic framework. Let $x$ be an element of a unital algebra over a commutative ring $R$ satisfying $x^{2} - t x + d 1 = 0.$ Then ever…

math.CO2026

A Dyadic Frequency Law for a Perturbed Hofstadter $Q$ -Recursion

Marco Mantovanelli

We study the perturbed Hofstadter $Q$ -recursion $Q (1) = Q (2) = 1, Q (n) = Q (n - Q (n - 1)) + Q (n - Q (n - 2)) + (- 1)^{n} (n \geq 3) .$ Cloître proved that the recursion is globally well-defi…

Averaged Extensions of Golomb's Triangular Recursion: Critical Invariance and Supercritical Constraints

Certified Return-Word Induction for a Perturbed Hofstadter Recursion

Quadratic Reduction and Classical Multiple-Index Fibonacci-Lucas Identities

A Dyadic Frequency Law for a Perturbed Hofstadter Q-Recursion

A Dyadic Frequency Law for a Perturbed Hofstadter $Q$ -Recursion