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Post Closed as "Not suitable for this site" by Mark Grant, Stefan Kohl♦, abx, Chris Godsil, S. Carnahan♦
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Roy van Rijn
Roy van Rijn
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I'm new to mathoverflow but hopefully anyone here can point me in the right direction.

The problem is as follows, imagine you have 4 beads, lets give them numbers 1,2,3,4. Now I want the unique necklaces without rotation, mirror nor duplication of the beads. So 1234 is the same as 3412 and 4321.

How do you call this sequence mathematically? It is related to a free necklace and to bracelet, but those include duplicate use of beads.

For N=1: 1
For N=2: 12 (same as 21)
For N=3: 123 (same as 132,231,213,321,312)
For N=4: 1234 1243 1324 (so not 1342 1423 1432, those are equal flipped)

Is there a good mathematical term for this set? And second: Is there a good way to construct the set for a given number?

I'm new to mathoverflow but hopefully anyone here can point me in the right direction.

The problem is as follows, imagine you have 4 beads, lets give them numbers 1,2,3,4. Now I want the unique necklaces without rotation, mirror nor duplication of the beads. So 1234 is the same as 3412 and 4321.

How do you call this sequence mathematically? It is related to a free necklace and to bracelet, but those include duplicate use of beads.

For N=1: 1
For N=2: 12 (same as 21)
For N=3: 123 (same as 132,231,213,321,312)
For N=4: 1234 1243 1324

Is there a good mathematical term for this set? And second: Is there a good way to construct the set for a given number?

I'm new to mathoverflow but hopefully anyone here can point me in the right direction.

The problem is as follows, imagine you have 4 beads, lets give them numbers 1,2,3,4. Now I want the unique necklaces without rotation, mirror nor duplication of the beads. So 1234 is the same as 3412 and 4321.

How do you call this sequence mathematically? It is related to a free necklace and to bracelet, but those include duplicate use of beads.

For N=1: 1
For N=2: 12 (same as 21)
For N=3: 123 (same as 132,231,213,321,312)
For N=4: 1234 1243 1324 (so not 1342 1423 1432, those are equal flipped)

Is there a good mathematical term for this set? And second: Is there a good way to construct the set for a given number?

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Roy van Rijn
Roy van Rijn
  • 131
  • 4

Terminology for beads/necklace/bracelet problem

I'm new to mathoverflow but hopefully anyone here can point me in the right direction.

The problem is as follows, imagine you have 4 beads, lets give them numbers 1,2,3,4. Now I want the unique necklaces without rotation, mirror nor duplication of the beads. So 1234 is the same as 3412 and 4321.

How do you call this sequence mathematically? It is related to a free necklace and to bracelet, but those include duplicate use of beads.

For N=1: 1
For N=2: 12 (same as 21)
For N=3: 123 (same as 132,231,213,321,312)
For N=4: 1234 1243 1324

Is there a good mathematical term for this set? And second: Is there a good way to construct the set for a given number?