Gennady Bachman

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20232026

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math.NT2026

Gaps of Binary Numerical Semigroups and of Binary Inclusion-Exclusion Polynomials

Gennady Bachman

Let $p$ be a given modulus, let $u$ be prime to $p$ , and consider the linear permutation $u \cdot n (mod p)$ of the residue system modulo $p$ . Writing $⟨ x ⟩_{p}$ to denote…

math.NT2026

On Heights and Diameters of Ternary Cyclotomic and Inclusion-Exclusion Polynomials

Gennady Bachman

For the $n$ th cyclotomic polynomial $Φ_{n}$ , let $A (n)$ denote the greatest absolute value of its coefficients, its height, and let $D (n)$ denote the difference between its largest a…

math.NT2023

A Note on Heights of Cyclotomic Polynomials

Gennady Bachman, Christopher Bao, Shenlone Wu

We show that for any positive integer $h$ , either $h$ or $h + 1$ is a height of some cyclotomic polynomial $Φ_{n}$ , where $n$ is a product of three distinct primes.