MULTICOLOR COMPOSITIONS AND CONJUGATION OF N- COLOR COMPOSITIONS

被引：0

作者：

Alanazi, Abdulaziz M. ^{[1
]}

Archibald, Margaret ^{[2
]}

Munagi, Augustine O. ^{[2
]}

机构：

[1] Univ Tabuk, Fac Sci, Dept Math, POB 741, Tabuk 71491, Saudi Arabia

[2] Univ Witwatersrand, John Knopfmacher Ctr Applicable Anal & Number Theo, Johannesburg, South Africa

来源：

CONTRIBUTIONS TO DISCRETE MATHEMATICS | 2024年 / 19卷 / 03期

关键词：

composition; multicolor composition; generating function; n- color composition;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce n-multicolor compositions which generalize the n-color compositions that Agarwal first defined twenty-two years ago. A summand may bear a set of many integer-valued colors which it bounds from above. We enumerate such multicolored compositions using generating functions. Then we isolate the conjugable class of multicolored compositions known as cracked compositions. A concise exposition of the conjugation of n-color compositions is presented in the classical tradition of Percy Alexander MacMahon (1854- 1929). Our set of conjugable n-color compositions turn out to be considerably larger than previously known ones.

引用

页码：68 / 85

页数：18

共 18 条

[1] Agarwal A.K., 2013, Ramanujan Math. Soc. Lect. Notes Ser., V20, P13
[2] ROGERS-RAMANUJAN IDENTITIES FOR PARTITIONS WITH N COPIES OF N
AGARWAL, AK
ANDREWS, GE
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 1987, 45 (01) : 40 - 49
[3] Agarwal AK, 2000, INDIAN J PURE AP MAT, V31, P1421
[4] Andrews GE., 1998, The Theory of Partitions
[5] Collins A, 2013, FIBONACCI QUART, V51, P130
[6] Guo YH, 2013, ARS COMBINATORIA, V109, P425
[7] Heubach S., 2010, Combinatorics of compositions and words
[8] Heubach S., 2004, Congr. Numer, V168, P127
[9] Hopkins B., 2012, Integers, V12B
[10] MacMahon P.A., 1915, Combinatory analysis, V1

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