Technion

Computer Science Colloquium

22/03/2011

Time+Place : Tuesday 22/03/2011 14:30 room 337-8 Taub  Bld.
Speaker    : Gil Barequet
Affiliation: Computer Science, Technion
Title      : Formulae and Growth Rates of High-Dimensional Polycubes

Abstract   :

A $d$-dimensional polycube of size $n$ is a $(d-1)$-face-connected set of
$n$ cubes in $d$ dimensions.  Fixed polycubes are considered distinct if
they differ in their shape or orientation.  A polycube \emph{proper} in $d$
dimensions cannot be embedded in less than $d$ dimensions.  In this talk I
will show a few closed formulae for fixed (proper and improper) polycubes,
and show that the growth-rate limit of the number of polycubes in $d$
dimensions is similar to $2ed-o(d)$ (estimated at $(2d-3)e+O(1/d)$) as $d$
tends to infinity.

Joint work with Ronnie Barequet (Math and Computer Science, TAU) and Guenter
Rote (Computer Science, FU).

Short Bio :

Gill Barequet is a faculty member at the Department of Computer Science of
the Technion (Israel Institute of Technology), Haifa.
He received his B.Sc. in Mathematics and Computer Science, and M.Sc.
and Ph.D. in Computer Science from Tel Aviv University in 1985, 1987, and
1994, respectively.
His research interests include discrete and computational geometry,
combinatorics, interpolation and reconstruction algorithms, and geometric
applications in various fields.
He holds five US patents in related areas.

Refreshments served from 14:15 on,
Lecture starts at 14:30

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