Parity of a permutation – Knowledge and References

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Topics from Linear Algebra

Published in Vladimir A. Dobrushkin, Applied Differential Equations, 2022

where the summation is over all n! permutations (i1,i2,…,in) of the integers 1,2,…,n and sign(σ) is ±1, which is determined by the parity of the permutation. Therefore, half of all the products in this sum are positive and half are negative.

Introduction

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Published in Vladimir A. Dobrushkin, Applied Differential Equations, 2018

Vladimir A. Dobrushkin

where the summation is over all permutations i1,i2,…,in of the integers 1,2,…,n and sign⁡(σ) is ±1, which is determined by the parity of the permutation. Therefore, half of all the products in this sum are positive and half are negative.

The Basic Formalism of Field Theory

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Published in A.N. Vasiliev, Patricia A. Millard, Functional Methods in Quantum Field Theory and Statistical Physics, 2019

A.N. Vasiliev, Patricia A. Millard

where ɛP = ± 1 depending on the parity of the permutation i1 … in → 1…n. The sum entering into (1.152) is det L, from which J = det L−1. Clearly, this form of J guarantees the validity of (1.151) for any function f(φ), since only the highest monomial contributes to the integral.

Ground state solutions to Hartree–Fock equations with magnetic fields

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Journal Information

Published in Applicable Analysis, 2018

C. Argáez, M. Melgaard

Here, is the set of all permutations of , and denotes the parity of the permutation p. The space is equipped with the scalar product