Abstract
We prove that Boolean functions on , whose Fourier transform is highly concentrated on irreducible representations indexed by partitions of whose largest part has size at least , are close to being unions of cosets of stabilizers of -tuples. We also obtain an edge-isoperimetric inequality for the transposition graph on which is asymptotically sharp for subsets of of size , using eigenvalue techniques. We then combine these two results to obtain a sharp edge-isoperimetric inequality for subsets of of size , where is large compared to , confirming a conjecture of Ben Efraim in these cases.
Original language | English |
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Journal | Forum of Mathematics, Sigma |
Volume | 5 |
DOIs | |
State | Published - 2017 |
ASJC Scopus subject areas
- Analysis
- Theoretical Computer Science
- Algebra and Number Theory
- Statistics and Probability
- Mathematical Physics
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Mathematics