Average site perimeter of directed animals on the two-dimensional lattices

Details Average site perimeter of directed animals on the two-dimensional lattices Average site perimeter of directed animals on the two-dimensional lattices

2009-06-24

arxiv.org/abs/0906.4536v3

Mathematics

Combinatorics

Scientific paper

We introduce new combinatorial (bijective) methods that enable us to compute the average value of three parameters of directed animals of a given area, including the site perimeter. Our results cover directed animals of any one-line source on the square lattice and its bounded variants, and we give counterparts for most of them in the triangular lattices. We thus prove conjectures by Conway and Le Borgne. The techniques used are based on Viennot's correspondence between directed animals and heaps of pieces (or elements of a partially commutative monoid).

Affiliated with

Also associated with

No associations

Rating

Average site perimeter of directed animals on the two-dimensional lattices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Average site perimeter of directed animals on the two-dimensional lattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Average site perimeter of directed animals on the two-dimensional lattices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-106559