Geodesic
Foulkes characters, Eulerian idempotents, and an amazing matrix
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 3, pp. 425-440.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: John Holte (Am. Math. Mon. 104:138-149, 1997) 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 (Brenti and Welker, Adv. Appl. Math. 42:545-556, 2009; Diaconis and Fulman, Am. Math. Mon. 116:788-803, 2009; Adv. Appl. Math. 43:176-196, 2009) and in the analysis of riffle shuffling (Diaconis and Fulman, Am. Math. Mon. 116:788-803, 2009; Adv. Appl. Math. 43:176-196, 2009). 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 (Cyclic Homology, 1992) 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.
Keywords: foulkes character, carry, Eulerian idempotent, symmetric group 
@article{JAC_2012__36_3_a2,
     author = {Diaconis, Persi and Fulman, Jason},
     title = {Foulkes characters, {Eulerian} idempotents, and an amazing matrix},
     journal = {Journal of Algebraic Combinatorics},
     pages = {425--440},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a2/}
}
TY  - JOUR
AU  - Diaconis, Persi
AU  - Fulman, Jason
TI  - Foulkes characters, Eulerian idempotents, and an amazing matrix
JO  - Journal of Algebraic Combinatorics
PY  - 2012
SP  - 425
EP  - 440
VL  - 36
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a2/
LA  - en
ID  - JAC_2012__36_3_a2
ER  - 
%0 Journal Article
%A Diaconis, Persi
%A Fulman, Jason
%T Foulkes characters, Eulerian idempotents, and an amazing matrix
%J Journal of Algebraic Combinatorics
%D 2012
%P 425-440
%V 36
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a2/
%G en
%F JAC_2012__36_3_a2
Diaconis, Persi; Fulman, Jason. Foulkes characters, Eulerian idempotents, and an amazing matrix. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 3, pp. 425-440. http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a2/