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What is Learnable in Valiant's Theory of the Learnable? 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Markov degree of the Birkhoff model
Takashi Yamaguchi, Mitsunori Ogawa, Akimichi Takemura · 2013-04-04 · via math.ST updates on arXiv.org

We prove the conjecture by Diaconis and Eriksson (2006) that the Markov degree of the Birkhoff model is three. In fact, we prove the conjecture in a generalization of the Birkhoff model, where each voter is asked to rank a fixed number, say r, of candidates among all candidates. We also give an exhaustive characterization of Markov bases for small r.

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