Efficient Counting and Asymptotics of k-Noncrossing Tangled Diagrams
By William Y.C. Chen, Jing Qin, Christian M. Reidys and Doron Zeilberger
.pdf
Appeared in the Elec. J. Combinatorics 16(1) (2009), R37.
Written: Feb. 23, 2008
Combinatorics is everywhere! In particular, in life itself. It turns out
that counting certain kinds of RNA configurations leads to tangled
enumeration problems.
Important: This article is accompanied by Maple
package
TANGLE
that computes and analyzes the sequences mentioned in the article.
Sample Input and Output
- To get the sequences for the number (k+1)-noncrossing tangled-diagrams of [n]
for k=1,2,3, for n from 1 to 1000 the, as well as linear recurrence equations and
asymptotics, the
input yields the
output.
- To get the sequences for the number (k+1)-noncrossing tangled-diagrams of [n]
for k=1,2,3,4,5 for n from 1 to 50, the
input yields the
output.
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