A necklace is a circular arrangement of beads which can be rotated and flipped without being considered a different arrangement. For example, there is only one necklace strung together from three beads where all beads have different colors.
a) How many different necklaces with N beads can be made with N distinct colors?
b) How many different necklaces can you string together if
you have to use 5 beads and up to 2 colors?
c) Now suppose we can only rotate necklaces, but not flip
them, so rotations are considered the same arrangement but flips
are considered different. Can you count the different necklaces
with N beads that can be made from a supply of 2 types of beads,
given that N is prime and the 2 types need not both be
used?
A necklace is a circular arrangement of beads which can be rotated and flipped without being considered a different arra...
A necklace is a circular arrangement of beads which can be rotated and flipped without being considered a different arrangement. For example, there is only one necklace strung together from three beads where all beads have different colors. a) How many different necklaces with N beads can be made with N distinct colors? b) How many different necklaces can you string together if you have to use 5 beads and up to 2 colors? c) Now suppose we can only...
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