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
StatePublished - 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

Factorization
Partition
Polynomial
Polynomial function
Theorem
Generating Function
Count
Odd

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
Andrews, George E. / The Alladi–Schur polynomials and their factorization. Analytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016. editor / George E. Andrews ; Frank Garvan. Springer New York LLC, 2017. pp. 25-38 (Springer Proceedings in Mathematics and Statistics).
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Andrews, GE 2017, The Alladi–Schur polynomials and their factorization. in GE Andrews & F Garvan (eds), Analytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016. Springer Proceedings in Mathematics and Statistics, vol. 221, Springer New York LLC, pp. 25-38, International Gainesville Number Theory Conference in Honor of Krishna Alladi’s 60th Birthday, 2016, Gainesville, United States, 3/17/16. https://doi.org/10.1007/978-3-319-68376-8_3

The Alladi–Schur polynomials and their factorization. / Andrews, George E.

Analytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016. ed. / George E. Andrews; Frank Garvan. Springer New York LLC, 2017. p. 25-38 (Springer Proceedings in Mathematics and Statistics; Vol. 221).

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

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