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In combinatorics there are there are special kind of sequences, in which their terms represent the number of different ways that we can draw chords with some properties.

Actually my question is motivated by the following examples of what I have mentioned earlier.

  1. Motzkin number (The number of different ways of drawing non-intersecting chords on a circle between n points)

  2. Bell number (the number of partitions of a set of size n, in this case the drawing of the chords is described in the link)

  3. Catalan number(number of non crossing partitions of some sets)

My question is that, can you, please, tell me similar sequences?

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  • $\begingroup$ oeis.org/search?q=chords&language=english&go=Search $\endgroup$ – Gerry Myerson May 14 '14 at 23:29
  • $\begingroup$ This should be community wiki as it is asking for any number of answers. There is no correct answer. $\endgroup$ – BWW May 15 '14 at 2:48
  • $\begingroup$ Perfect matchings. Perfect matchings with restrictions on the crossing number and or on the nesting number. $\endgroup$ – BWW May 15 '14 at 2:50
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    $\begingroup$ You linked to the Wikipedia page on Bell numbers. I see no "drawing of chords" there and searches of the page for "chord" and "matching" give no hits. How are Bell numbers counts of ways to draw chords? $\endgroup$ – Douglas Zare May 15 '14 at 3:55
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    $\begingroup$ To put it more clearly: Bell numbers count the systems of chords that can be drawn in such a way that every pair of chords sharing an endpoint is part of a triangle. $\endgroup$ – David Eppstein May 15 '14 at 21:38
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You should at least include the double factorials (chord diagrams in which each of $2n$ points has exactly one chord incident to it — apparently these are also called Brauer diagrams).

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  • $\begingroup$ Thank you this kind of examples is what I am looking for $\endgroup$ – math137 May 15 '14 at 9:55

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