Murray R. Bremner

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20182026

most citedHigher polynomial identities for mutations of associative algebras

1 citations · 1 across the 6 of their papers we have counts for

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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

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.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…

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)

The Veronese square of the dendriform operad

Operator identities of multiplicity 3 for associative algebras

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