Georgy P. Egorychev, “Permanents as formulas of summation over an algebra with a unique <nobr>$n$</nobr>-ary operation”, J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 6,Pages <nobr>796

This article is cited in 1 paper

Permanents as formulas of summation over an algebra with a unique $n$-ary operation

Georgy P. Egorychev

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny 79, Krasnoyarsk, 660041, Russia

Abstract: We give a new general definition for permanents over an algebra with a unique $n$-ary operation and study their properties. In particular, it is shown that properties of these permanents coincide with the basic properties of the classical Binet–Cauchy permanent (1812).

Keywords: permanents, noncommutative and multioperator algebras, the polarization theorem, polynomial identities.

UDC: 517.55 + 519.1

Received: 22.06.2018
Received in revised form: 08.09.2018
Accepted: 04.11.2018

Language: English

DOI: 10.17516/1997-1397-2018-11-6-796-799