Displaying similar documents to “On the Permanent of a Matrix”

Basic Properties of Determinants of Square Matrices over a Field 1

Karol Pąk (2007)

Formalized Mathematics

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In this paper I present basic properties of the determinant of square matrices over a field and selected properties of the sign of a permutation. First, I define the sign of a permutation by the requirement [...] where p is any fixed permutation of a set with n elements. I prove that the sign of a product of two permutations is the same as the product of their signs and show the relation between signs and parity of permutations. Then I consider the determinant of a linear combination...

Axial permutations of ω²

Paweł Klinga (2016)

Colloquium Mathematicae

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We prove that every permutation of ω² is a composition of a finite number of axial permutations, where each axial permutation moves only a finite number of elements on each axis.

Some new facts about group 𝒢 generated by the family of convergent permutations

Roman Wituła, Edyta Hetmaniok, Damian Słota (2017)

Open Mathematics

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The aim of this paper is to present some new and essential facts about group 𝒢 generated by the family of convergent permutations, i.e. the permutations on ℕ preserving the convergence of series of real terms. We prove that there exist permutations preserving the sum of series which do not belong to 𝒢. Additionally, we show that there exists a family G (possessing the cardinality equal to continuum) of groups of permutations on ℕ such that each one of these groups is different than...