The Alladi–Schur polynomials and their factorization

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

K. Alladi first observed the following variant of I. Schur’s 1926 partition theorem. Namely, the number of partitions of n in which all parts are odd and none appears more than twice equals the number of partitions of n in which all parts differ by at least 3 and more than 3 if one of the parts is a multiple of 3. Subsequently, the theorem was refined to count also the number of parts in the relevant partitions. In this paper, a surprising factorization of the related polynomial generating functions is developed.

Original languageEnglish (US)
Title of host publicationAnalytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016
EditorsGeorge E. Andrews, Frank Garvan
PublisherSpringer New York LLC
Pages25-38
Number of pages14
ISBN (Print)9783319683751
DOIs
Publication statusPublished - Jan 1 2017
EventInternational Gainesville Number Theory Conference in Honor of Krishna Alladi’s 60th Birthday, 2016 - Gainesville, United States
Duration: Mar 17 2016Mar 21 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume221
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherInternational Gainesville Number Theory Conference in Honor of Krishna Alladi’s 60th Birthday, 2016
CountryUnited States
CityGainesville
Period3/17/163/21/16

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Andrews, G. E. (2017). The Alladi–Schur polynomials and their factorization. In G. E. Andrews, & F. Garvan (Eds.), Analytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016 (pp. 25-38). (Springer Proceedings in Mathematics and Statistics; Vol. 221). Springer New York LLC. https://doi.org/10.1007/978-3-319-68376-8_3