Eulerian polynomial identities on matrix rings

Szigeti, Jenő and Tuza, Zsolt and Révész, Gábor (1993) Eulerian polynomial identities on matrix rings. JOURNAL OF ALGEBRA, 161 (1). pp. 90-101. ISSN 0021-8693

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Abstract

We prove that [formula] is a polynomial identity on Mn(Ω) over any commutative ring Ω with 1; here Γ is an Eulerian directed graph with k vertices and N edges, N ≥ 2kn, and Π(Γ) is the set of covering directed paths of Γ (viewed as permutations with respect to an arbitrary but fixed ordering of the edges of Γ). The standard and double Capelli identities can be obtained from extremely simple Eulerian graphs. © 1993 Academic Press. All rights reserved.

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