Compositions with a fixed number of inversions
| dc.article.end-page | 617 | |
| dc.article.start-page | 601 | |
| dc.contributor.author | Knopfmacher, A. | |
| dc.contributor.otherauthor | Mays, M. E. | |
| dc.contributor.otherauthor | Wagner, S. | |
| dc.date.accessioned | 2025-04-23T12:42:50Z | |
| dc.date.issued | 2018-05 | |
| dc.description.abstract | A composition of the positive integer n is a representation of n as an ordered sum of positive integers n = a1 + a2 + ··· + am. There are 2n−1 unrestricted compositions of n, which can be sorted according to the number of inversions they contain. (An inversion in a composition is a pair of summands {ai, aj} for which i<j and ai > aj .) The number of inversions of a composition is an indication of how far the composition is from a partition of n, which by convention uses a sequence of nondecreasing summands and thus has no inversions. We count compositions of n with exactly r inversions in several ways to derive generating function identities, and also consider asymptotic results. | |
| dc.description.sponsorship | National Research Foundation. | |
| dc.description.submitter | PM2025 | |
| dc.faculty | Faculty of Science | |
| dc.identifier | 0000-0003-1962-043X | |
| dc.identifier.citation | Knopfmacher, A., Mays, M.E. & Wagner, S. Compositions with a fixed number of inversions. Aequat. Math. 93, 601–617 (2019). https://doi.org/10.1007/s00010-018-0563-6 | |
| dc.identifier.issn | 0001-9054 (print) | |
| dc.identifier.issn | 1420-8903 (online) | |
| dc.identifier.other | 10.1007/s00010-018-0563-6 | |
| dc.identifier.uri | https://hdl.handle.net/10539/44841 | |
| dc.journal.title | Aequationes Mathematicae | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.relation.ispartofseries | Vol.93 | |
| dc.rights | © Springer International Publishing AG, part of Springer Nature 2018. | |
| dc.school | School of Mathematics | |
| dc.subject | Composition | |
| dc.subject | Partition | |
| dc.subject | Inversion | |
| dc.subject.primarysdg | N/A | |
| dc.title | Compositions with a fixed number of inversions | |
| dc.type | Article |