Some n-Color Compositions
نویسنده
چکیده
In the classical theory of partitions, compositions were first defined by MacMahon [1] as ordered partitions. For example, there are 5 partitions and 8 compositions of 4. The partitions are 4, 31, 22, 21, 1 and the compositions are 4, 31, 13, 22, 21, 121, 12, 1. Agarwal and Andrews [2] defined an n-color partition as a partition in which a part of size n can come in n different colors. They denoted different colors by subscripts: n1, n2, . . ., nn. Analogous to MacMahon’s ordinary compositions Agarwal [3] defined an n-color composition as an n-color ordered partition. Thus, for example, there are 21 n-color compositions of 4, viz.,
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