COMPOSITIONS AS NON-ALTERNATING SEQUENCES OF PARTITIONS

Applicable Analysis and Discrete Mathematics

article

Aubrey Blecher¹  Charlotte Brennan²  Toufik Mansour³ 

[1] School of Mathematics, University of the Witwatersrand, Private Bag 3;The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3;Department of Mathematics, Univer

关键词: Compositions;    partitions;    generating functions;   

DOI  :  10.2298/AADM130515008B

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Compositions are conceptualized as non alternating sequences of blocks ofnon-decreasing and strictly decreasing partitions. We find the generatingfunction F(x, y, q) where x marks the size of the composition, y the numberof parts and q the number of such partition blocks minus 1. We form theseblocks starting on the left-hand-side of the composition and maximizing thesize of each block. We also find the generating function for the total numberof such blocks.

【 授权许可】

Unknown