RNAshapes
Supplement to "Asymptotics of RNA shapes"
by W.A. Lorenz, Y. Ponty and P. Clote, submitted
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supplementary.pdf: PDF file with
complete proof, including all details, for the number of pi-shapes
compatible with an RNA sequence of length n, assuming that any base
can basepair with any other base, and that there are at least 3
unpaired bases in each hairpin loop.
Mathematica code and html files for various computations
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Number of pi-shapes of length n:
HTML,
Mathematica code
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Number of pi-shapes compatible with length n secondary structures:
HTML,
Mathematica code
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Number of piPrime-shapes of length n:
HTML,
Mathematica code
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Number of piPrime-shapes compatible with length n secondary structures:
HTML,
Mathematica code
Maple code and html files for various computations
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Combinatorial proof of a one-to-one correspondence between pi-shapes and Motzkin words [html][Maple]
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A linear recurrence for the number of pi-shapes [html][Maple]