Neal Madras - York University
Enumeration Bounds via an Isoperimetric-Type Inequality
In 1949, Loomis and Whitney published a geometrically intuitiveinequality that bounds the cardinality of a d-dimensional setin terms of the cardinalities of its projections onto thecoordinate hyperplanes. We show how this inequality can be usedto prove two results in the asymptotic enumeration of lattice animals:a bound on the critical exponent for the number of lattice animalsin arbitrary dimension (Madras, 1995), and a bound on the growthconstant for the number of "almost unknotted" embeddings of graphsin the cubic lattice (in preparation, with Sumners and Whittington).