On the Asymptotic Enumeration of LEGO Structures

Abstract

We investigate experimentally the growth regimes of the number of LEGO structures that can be constructed contiguously from n blocks of equal shape and color.

2000 AMS Subject Classification:

• 05A16
• 05-04

Keywords:

• asymptotic enumeration
• LEGO
• Monte Carlo methods

ACKNOWLEDGMENTS

We are grateful to colleagues at the Department of Mathematical Sciences at the University of Copenhagen for fruitful discussions, notably Bergfinnur Durhuus, Ernst Hansen, and Niels Richard Hansen, as well as the entire computing department, led by Rasmus Borup Hansen, for their help in keeping our rather demanding processes alive. We also wish to extend our thanks to all the people involved in the LDraw project, from which we have benefited in an obvious way.