Geodesic
Fredman's reciprocity, invariants of Abelian groups, and the permanent of the Cayley table.
Journal of Algebraic Combinatorics, Tome 33 (2011) no. 1, pp. 111-125.

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

Summary: Let $C _{ n}$ mathcalC_n denote the cyclic group of order $n$. For $G= C _{ n}$ G=mathcalC_n, we compute the Poincaré series of all $C _{ n}$ mathcalC_n-isotypic components in $### (the symmetric tensor exterior algebra of ###)$. From this we derive a general reciprocity and some number-theoretic identities. This generalises results of Fredman and Elashvili-Jibladze. Then we consider the Cayley table, $###$, of $G$ and some generalisations of it. In particular, we prove that the number of formally different terms in the permanent of $###$ equals $###$, where $n$ is the order of $G$.
Keywords: keywords molien formula, Poincaré series, permanent, Ramanujan's sum 
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     author = {Panyushev, Dmitri I.},
     title = {Fredman's reciprocity, invariants of {Abelian} groups, and the permanent of the {Cayley} table.},
     journal = {Journal of Algebraic Combinatorics},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2011__33_1_a3/}
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Panyushev, Dmitri I. Fredman's reciprocity, invariants of Abelian groups, and the permanent of the Cayley table.. Journal of Algebraic Combinatorics, Tome 33 (2011) no. 1, pp. 111-125. http://geodesic.mathdoc.fr/item/JAC_2011__33_1_a3/