Counting interlacing pairs on the circle
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.
|Permutations, words, matrices (msc 05A05), Exact enumeration problems, generating functions (msc 05A15)|
|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.