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Hierarchical models, marginal polytopes, and linear codes

Thomas Kahle, Walter Wenzel, Nihat Ay (2009)

Kybernetika

In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.

Hoeffding spaces and Specht modules

Giovanni Peccati, Jean-Renaud Pycke (2011)

ESAIM: Probability and Statistics

It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.

Hoeffding spaces and Specht modules

Giovanni Peccati, Jean-Renaud Pycke (2011)

ESAIM: Probability and Statistics

It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.

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