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Entropy, independent sets and antichains: A new approach to Dedekind's problem |
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| Authors: | Jeff Kahn |
| Institution: | Department of Mathematics and RUTCOR, Rutgers University, New Brunswick, New Jersey 08903 |
| Abstract: | For |
| Keywords: | Entropy independent set antichain Dedekind's Problem |
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-regular, 
-vertex bipartite graphs with bipartition 
, a precise bound is given for the sum over independent sets 
of the quantity 
. (In other language, this is bounding the partition function for certain instances of the hard-core model.) This result is then extended to graded partially ordered sets, which in particular provides a simple proof of a well-known bound for Dedekind's Problem given by Kleitman and Markowsky in 1975.