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We present an orthogonal basis for functions over a slice of the Boolean hypercube.
Logarithmic Sobolev inequalities
Leonard Gross · 1975
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A Krawtchouk polynomial addition theorem and wreath products of symmetric groups
Charles F. Dunkl · 1976
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An addition theorem for Hahn polynomials: the spherical functions
Charles F. Dunkl · 1978
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Orthogonal functions on some permutation groups
Charles F. Dunkl · 1979
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On the Shannon capacity of a graph
László Lovász · 1979
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Algebraic Combinatorics I: Association schemes
Eiichi Bannai and Tatsuro Ito · 1984
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The exact bound in the Erdős-Ko-Rado theorem
Richard M. Wilson · 1984
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The influence of variables on Boolean functions
Jeff Kahn, Gil Kalai, and Nati Linial · 1988
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Old and new proofs of the Erdős-Ko-Rado theorem
Péter Frankl and Ron L. Graham · 1989
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On the degree of Boolean functions as real polynomials
Noam Nisan and Mario Szegedy · 1994
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Boolean functions with low average sensitivity depend on few coordinates
Ehud Friedgut · 1998
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Logarithmic Sobolev inequality for some models of random walks
Tzong-Yau Lee and Horng-Tzer Yau · 1998
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Boolean functions whose Fourier transform is concentrated on the first two levels
Ehud Friedgut, Gil Kalai, and Assaf Naor · 2002
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Property testing, PCP and Juntas
Guy Kindler · 2002
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Noise-resistant Boolean functions are juntas, 2004
Guy Kindler and Shmuel Safra · 2004
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Symmetric chains, Gelfand–Tsetlin chains, and the Terwilliger algebra of the binary Hamming scheme
Murali K. Srinivasan · 2011
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KKL, Kruskal–Katona, and monotone nets
Ryan O’Donnell and Karl Wimmer · 2013
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Sharpness of KKL on Schreier graphs
Ryan O’Donnell and Karl Wimmer · 2013
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Friedgut–Kalai–Naor theorem for slices of the Boolean cube, 2014
Yuval Filmus · 2014
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Analysis of Boolean Functions
Ryan O’Donnell · 2014
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Low influence functions over slices of the Boolean hypercube depend on few coordinates
Karl Wimmer · 2014
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A new approach to the representation theory of the symmetric groups — II
Anatoly Vershik and Andrei Okounkov · 2005
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KKL, Kruskal–Katona, and monotone nets
Ryan O’Donnell and Karl Wimmer · 2009
Cited alongside, same era.
Noise stability of functions with low influences: Invariance and optimality
Elchanan Mossel, Ryan O’Donnell, and Krzysztof Oleszkiewicz · 2010
Cited alongside, same era.
Yuval Filmus, Guy Kindler, Elchanan Mossel, and Karl Wimmer · 2015
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Harmonicity and invariance on slices of the Boolean cube, 2015
Yuval Filmus and Elchanan Mossel · 2015
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