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On the Spectral Properties of Symmetric Functions

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arxiv 1704.03176 v1 pith:ZCKJC7KY submitted 2017-04-11 cs.CC math.FA

Anil Ada (CMU) , Omar Fawzi (LIP) , Raghav Kulkarni This is my paper · ORCID
classification cs.CCmath.FA
keywords complexityfunctionsapproximatecharacterizationmonomialconjecturenormsign
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We characterize the approximate monomial complexity, sign monomial complexity , and the approximate L 1 norm of symmetric functions in terms of simple combinatorial measures of the functions. Our characterization of the approximate L 1 norm solves the main conjecture in [AFH12]. As an application of the characterization of the sign monomial complexity, we prove a conjecture in [ZS09] and provide a characterization for the unbounded-error communication complexity of symmetric-xor functions.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 4 citations worldwide. Full citation record

  1. A Paturi Theorem for Signed Subcube Representations

    cs.CC 2026-08 conditional novelty 7.0 of 10

    For symmetric Boolean functions, approximate signed-subcube weight is 2^Theta(D) and sparsity is 2^Theta(D) log n up to log factors, where D is the deepest transition depth.

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