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arXiv · 1102.5159

Foulkes Characters, Eulerian Idempotents, and an Amazing Matrix

Persi Diaconis·Jason Fulman
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Abstract

John Holte [16] introduced a family of "amazing matrices" which give the transition probabilities of "carries" when adding a list of numbers. It was subsequently shown that these same matrices arise in the combinatorics of the Veronese embedding of commutative algebra [4,6,7] and in the analysis of riffle shuffling [6,7]. We find that the left eigenvectors of these matrices form the Foulkes character table of the symmetric group and the right eigenvectors are the Eulerian idempotents introduced by Loday [20] in work on Hochschild homology. The connections give new closed formulae for Foulkes characters and allow explicit computation of natural correlation functions in the original carries problem.

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Persi Diaconis, Jason Fulman. 2011-02-25. Foulkes Characters, Eulerian Idempotents, and an Amazing Matrix. https://arxiv.org/abs/1102.5159

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