Beaded partitions with k colors

In this paper a new category of partitions called beaded partitions with k colors will be introduced. The generating functions for these partitions will be given and several properties and congruences will be presented. A beaded partition of a positive integer n is a necklace made up of strands of beads in k colors where the total number of beads in the necklace is n. Sliding the beads around the strand does not change the strand and changing the order of the strands in the necklace does not change the partition. However, flipping a strand can result in a different strand. For example if k = 2 then there are two distinct strands with one bead, three distinct strands with two beads, and four distinct strands with three beads which are illustrated in Figure 1. Figure 1. Beaded Strands with 2 Colors. Note that the three strands in Figure 2 are equivalent since the beads can be slid around the strand to form each of these color configurations. Received by the editors March 2, 2011, and in revised form August 10, 2011. 2000 Mathematics Subject Classification. 05A05.