Combinatorics of certain restricted -color composition functions

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• 作者：R. Sachdeva ^{rachna.sachdeva.1989@gmail.com} ; A.K. Agarwal ; ^aka@pu.ac.in
• 关键词：nn-color compositions ; Integer sequences ; Generating functions ; Explicit formulas ; Recurrence relations ; Augmented skinny trees ; Binary words ; Combinatorial identities
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：340
• 期：3
• 页码：361-372
• 全文大小：927 K
• 卷排序：340

文摘

Analogous to MacMahon’s definition of compositions, the second author, 2000, defined nn-color compositions as nn-color ordered partitions. Several combinatorial properties of nn-color compositions were subsequently found by him, 2003, G. Narang and A.K. Agarwal, 2006, 2008, and C. Shapcott, 2012. Recently, Y. Guo 2012, 2013, studied three restricted nn-color composition functions and found generating functions, explicit formulas and recurrence relations for them. In this paper, we introduce nine new restricted nn-color composition functions. It is then shown that three of them are equal to three other functions. Eventually, here we study six integer sequences from the combinatorial point of view. In addition to generating functions, explicit formulas and recurrence relations for each of them, we also obtain six combinatorial identities involving different nn-color composition functions. The main results of this paper are contained in Section 3.