Geodesic
Partition identities. I: Sandwich theorems and logical 0-1 laws
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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The Sandwich Theorems proved in this paper give a new method to show that the partition function $a(n)$ of a partition identity $$ {\bf A}(x) \ :=\ \sum_{n=0}^\infty a(n)x^n\ =\ \prod_{n=1}^\infty (1-x^n)^{-p(n)} $$ satisfies the condition RT$_1$ $$ \lim_{n\rightarrow \infty}{a(n-1)\over a(n)} \ =\ 1\,. $$ This leads to numerous examples of naturally occuring classes of relational structures whose finite members enjoy a logical 0–1 law.
DOI : 10.37236/1802
Classification : 03C13, 05A16, 11P81
Mots-clés : partition identity, relational structures, logical 0-1 law 
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     author = {Jason P. Bell and Stanley N. Burris},
     title = {Partition identities. {I:} {Sandwich} theorems and logical 0-1 laws},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1802},
     zbl = {1057.03024},
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Jason P. Bell; Stanley N. Burris. Partition identities. I: Sandwich theorems and logical 0-1 laws. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1802

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