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Title: To dry perchance to live: Insights from the genome of the desiccation‐tolerant biocrust moss Syntrichia caninervis
Award ID(s):
1840931 1638966 1638972 1444448 1638956
PAR ID:
10208235
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ; ; ;
Date Published:
Journal Name:
The Plant Journal
ISSN:
0960-7412
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. The 1971 Fortuin–Kasteleyn–Ginibre inequality for two monotone functions on a distributive lattice is well known and has seen many applications in statistical mechanics and other fields of mathematics. In 2008, one of us (Sahi) conjectured an extended version of this inequality for all n > 2 monotone functions on a distributive lattice. Here, we prove the conjecture for two special cases: for monotone functions on the unit square in [Formula: see text] whose upper level sets are k-dimensional rectangles and, more significantly, for arbitrary monotone functions on the unit square in [Formula: see text]. The general case for [Formula: see text], remains open. 
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