Refinement for sequences in partitions

Refinement for sequences in partitions

The k -measure of an integer partition was recently introduced by Andrews, Bhattacharjee, and Dastidar. They established an unexpected nice result, which states that the number of partitions of n with 2-measure m is equal to the number of partitions of n with Durfee square of side m . In this note,...

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Veröffentlicht in:The Ramanujan journal 2023, Vol.60 (1), p.175-180
Hauptverfasser: Lin, Bernard L. S., Lin, Xiaowei
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Zusammenfassung:The k -measure of an integer partition was recently introduced by Andrews, Bhattacharjee, and Dastidar. They established an unexpected nice result, which states that the number of partitions of n with 2-measure m is equal to the number of partitions of n with Durfee square of side m . In this note, we aim to obtain the refinement of their result, which involves two statistics, the smallest part and the length of partitions.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-022-00554-8