Formulae and growth rates of high-dimensional polycubes

גיל ברקת (מדעי המחשב, הטכניון)
יום ראשון, 18.5.2008, 14:00
חדר 337, בניין טאוב למדעי המחשב

A $d$-dimensional polycube is a connected set of $d$-dimensional cubes on an orthogonal lattice, where connectivity is through $(d-1)$-dimensional faces. A polycube is said to be proper in $d$ dimensions if it spans all the $d$ dimensions, that is, the convex hull of the centers of all its cubes is $d$-dimensional.

We prove a few new formulae for the numbers of (proper and total) polycubes, and show that (2d-3)e + O(1/d) is the asymptotic growth rate of the number of $d$-dimensional polycube.

Joint work with Ronnie Barequet (Math and Computer Science, Tel Aviv Univ.).

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