Strong Fermion Interactions in Fractional Quantum Hall States by Shashikant Mulay & John J. Quinn & Mark Shattuck

Author:Shashikant Mulay & John J. Quinn & Mark Shattuck
Language: eng
Format: epub
ISBN: 9783030004941
Publisher: Springer International Publishing

4.Let be the set of all such that g is homogeneous of degree m in .

5.Let , where each is a nonnegative integer. Define to be the set of all such that the -degree of g is for .

Remarks

1.If and , then observe that is homogeneous of degree m in , where and the -degree of is for .

2.For E(N, V) to be nonempty, it is necessary that is an even integer and for . Clearly, E(2, V) is nonempty if and only if . In general, we are not aware of any conditions on (N, V) that are known to be necessary and sufficient for E(N, V) to be nonempty. Presently, we merely point out the following obvious fact. Suppose is an even integer. Let be the set of all ordered -tuples of integers such that for and . Given , let and observe that the sum is also an even integer. Then the cardinality of E(N, V) equals the sum of the cardinalities of as a ranges over .

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