Murray R. Bremner

collaborators

5 papers

math.CO2026

Enumerating Multi-Operator Monomials in Commutative and Noncommutative Settings

Yu Hin Au, Murray R. Bremner

We study enumeration problems for multi-operator monomials generated from one indeterminate by an associative multiplication together with finitely many unary operators. We conside…

math.RA2026

The Veronese square of the dendriform operad

Murray R. Bremner

Veronese powers of operads were introduced in 2020 By Dotsenko, Markl, and Remm \cite{DMR}. The $m$ -th Veronese power of a weight-graded operad $V$ is the suboperad $\mat…

math.CO2025

A new generalization of the Narayana numbers inspired by linear operators on associative $d$ -ary algebras

Yu Hin Au, Murray R. Bremner

We introduce and study a generalization of the Narayana numbers $N_{d} (n, k) = \frac{1}{n + 1} (k + 1 n + 1) (k n + ( n - k ) ( d - 2 ) + 1)$ for integers $d \geq 2$ and $n, k \geq 0$ . T…

math.RA2025

Algebraic identities for linear operators on associative triple systems (long version)

Murray R. Bremner

We present the first classification of algebraic identities in 3 variables for linear operators on associative structures. We work in the context of associative triple systems, but…

math.RA2025

Operator identities of multiplicity 3 for associative algebras

Murray R. Bremner

We consider algebraic identities for linear operators on associative algebras in which each term has degree 2 (the number of variables) and multiplicity 3 (the number of occurrence…

Enumerating Multi-Operator Monomials in Commutative and Noncommutative Settings

The Veronese square of the dendriform operad

A new generalization of the Narayana numbers inspired by linear operators on associative d-ary algebras

Algebraic identities for linear operators on associative triple systems (long version)

Operator identities of multiplicity 3 for associative algebras

A new generalization of the Narayana numbers inspired by linear operators on associative $d$ -ary algebras