Let be the number of interlacing chords joining points on the circle. Let . Then . This formula was conjectured by J. Betramas. The number is also the number of interlacing involutions of points on the real line.

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CWI
Department of Analysis, Algebra and Geometry [AM]

Hazewinkel, M, & Kalashnikov, V.V. (1995). Counting interlacing pairs on the circle. Department of Analysis, Algebra and Geometry [AM]. CWI.