Mario DeFranco

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20182026

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1 citations · 1 across the 10 of their papers we have counts for

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math.CO2026

On Boolean polynomials and the Union-Closed Conjecture

Mario DeFranco

For a set of $m$ subsets of a universe set of size $n$ , we construct a Boolean polynomial $ICC_{m, n} (X)$ such that the Union-Closed Conjecture is true for this $m$ and $n$ …

math.CO2019

On a series for the upper incomplete Gamma function

Mario DeFranco

We define an absolutely convergent series for the upper incomplete Gamma function $Γ (s, z)$ for $z \geq 1$ and $s \in C$ . We express this series using certain polynomials whi…

math.CO2019

A Constructive Proof of Jacobi's Identity for the Sum of Two Squares

Mario DeFranco

We present a constructive proof of Jacobi's identity for the sum of two squares. We present a combinatorial proof of the Jacobi Triple Product and combine with a proof of Hirschhor…

math.CO2019

On $q$ -analogues Arising from Elliptic Integrals and the Arithmetic-Geometric Mean

Mario DeFranco

We prove $q$ -analogues of identities that are equivalent to the functional equation of the arithmetic-geometric mean. We also present $q$ -analogues of $F (k, \frac{π}{2})$ , the…

On Boolean polynomials and the Union-Closed Conjecture

On a series for the upper incomplete Gamma function

A Constructive Proof of Jacobi's Identity for the Sum of Two Squares

On q-analogues Arising from Elliptic Integrals and the Arithmetic-Geometric Mean

On $q$ -analogues Arising from Elliptic Integrals and the Arithmetic-Geometric Mean