# ALGEBRAIC COMBINATORICS

On the $k$-measure of partitions and distinct partitions
Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1353-1361.

The $k$-measure of an integer partition was recently introduced by Andrews, Bhattacharjee and Dastidar. In this paper, we establish trivariate generating function identities counting both the length and the $k$-measure for partitions and distinct partitions, respectively. The $2$-measure case for partitions extends a result of Andrews, Bhattacharjee and Dastidar.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.253
Classification: 11P84,  05A17
Keywords: partition, distinct partition, generating function, $k$-measure, Durfee square
Andrews, George E. 1; Chern, Shane 2; Li, Zhitai 1

1 Penn State University Department of Mathematics University Park PA 16802 (USA)
2 Dalhousie University Department of Mathematics and Statistics Halifax Nova Scotia, B3H 4R2 (Canada)
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Andrews, George E.; Chern, Shane; Li, Zhitai. On the $k$-measure of partitions and distinct partitions. Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1353-1361. doi : 10.5802/alco.253. https://alco.centre-mersenne.org/articles/10.5802/alco.253/

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