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A Note on the Length of Trivectors
Published online by Cambridge University Press: 20 November 2018
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This note concerns elements (called trivectors) of the third Grassmann product of a complex vector space U. Usually there are many ways to write a given trivector as the sum of simple or decomposable trivectors, and it is an interesting problem to find those representations which contain the smallest possible number of decomposables. This number we shall call the length of the trivector. Let N(n) denote the length of the longest trivector in ∧3U where U has dimension n. In this note we give upper bounds for N(n) when n ≤ 8.
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- Copyright © Canadian Mathematical Society 1978
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