Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-08T04:39:37.034Z Has data issue: false hasContentIssue false
  • English
  • Français

GENERALISATION OF A RESULT ON DISTINCT PARTITIONS WITH BOUNDED PART DIFFERENCES

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  24 July 2019

RUNQIAO LI Open the ORCID record for RUNQIAO LI [Opens in a new window] ,
BERNARD L. S. LIN Open the ORCID record for BERNARD L. S. LIN [Opens in a new window]  and
ANDREW Y. Z. WANG Open the ORCID record for ANDREW Y. Z. WANG [Opens in a new window]
RUNQIAO LI
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China email runqiaoli@outlook.com
BERNARD L. S. LIN
Affiliation:
School of Science, Jimei University, Xiamen 361021, PR China email linlsjmu@163.com
ANDREW Y. Z. WANG*
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China email yzwang@uestc.edu.cn
*
✉yzwang@uestc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We generalise a result of Chern [‘A curious identity and its applications to partitions with bounded part differences’, New Zealand J. Math. 47 (2017), 23–26] on distinct partitions with bounded difference between largest and smallest parts. The generalisation is proved both analytically and bijectively.

Keywords

partitiondistinct partitionbounded part difference

MSC classification

Primary: 11P84: Partition identities; identities of Rogers-Ramanujan type
Secondary: 05A17: Partitions of integers
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 2 , April 2020 , pp. 233 - 237
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This work was supported by the National Natural Science Foundation of China (Nos. 11401080 and 11871246).

References

Andrews, G. E., The Theory of Partitions (Cambridge University Press, New York, 1998).Google Scholar
Andrews, G. E., Beck, M. and Robbins, N., ‘Partitions with fixed differences between largest and smallest parts’, Proc. Amer. Math. Soc. 143 (2015), 4283–4289.Google Scholar
Breuer, F. and Kronholm, B., ‘A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins’, Res. Number Theory 2 (2016), Article 2, 15 pages.Google Scholar
Chapman, R., ‘Partitions with bounded differences between largest and smallest parts’, Australas. J. Combin. 64 (2016), 376–378.Google Scholar
Chern, S., ‘A curious identity and its applications to partitions with bounded part differences’, New Zealand J. Math. 47 (2017), 23–26.Google Scholar
Chern, S., ‘An overpartition analogue of partitions with bounded differences between largest and smallest parts’, Discrete Math. 340 (2017), 2834–2839.Google Scholar
Chern, S. and Yee, A. J., ‘Overpartitions with bounded part differences’, Eur. J. Combin. 70 (2018), 317–324.Google Scholar
Lin, B. L. S., ‘$k$-regular partitions with bounded differences between largest and smallest parts’, Preprint.Google Scholar
Lin, B. L. S., ‘Refinements of the results on partitions and overpartitions with bounded part differences’, Preprint.Google Scholar