Arithmetic partition sums and orbits of Z_n^k under the symmetric group S_k

Simple item page
dc.creatorBeck, Matthias
dc.creatorFeingold, Alex J.
dc.creatorWeiner, Michael D.
dc.date2001-06-29
dc.date2001-07-22
dc.date.accessioned2026-07-07T04:42:24Z
dc.date.available2026-07-07T04:42:24Z
dc.descriptionWe study M(n,k,r), the number of orbits of {(a_1,...,a_k)\in Z_n^k | a_1+...+a_k = r (mod n)} under the action of S_k. Equivalently, M(n,k,r) sums the partition numbers of an arithmetic sequence: M(n,k,r) = sum_{t \geq 0} p(n-1,k,r+nt), where p(a,b,t) denotes the number of partitions of t into at most b parts, each of which is at most a. We derive closed formulas and various identities for such arithmetic partition sums. These results have already appeared in Elashvili/Jibladze/Pataraia, Combinatorics of necklaces and "Hermite reciprocity", J. Alg. Combin. 10 (1999) 173-188, and the main result was also published by Von Sterneck in Sitzber. Akad. Wiss. Wien. Math. Naturw. Class. 111 (1902), 1567-1601 (see Lemma 2 and references in math.NT/9909121). Thanks to Don Zagier and Robin Chapman for bringing these references to our attention.
dc.descriptionThis paper has been withdrawn by the authors because the results have already appeared elsewhere
dc.identifierhttps://arxiv.org/abs/math/0106267
dc.identifierhttp://arxiv.org/abs/math/0106267
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61769
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11P81, 5A17 (Primary) 5A15, 11B65 (Secondary)
dc.titleArithmetic partition sums and orbits of Z_n^k under the symmetric group S_k
dc.typetext

Files

Collections

arXiv