scholarly journals Proof of the Razumov–Stroganov Conjecture for some Infinite Families of Link Patterns

10.37236/1136 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
P. Zinn-Justin
Keyword(s):  
Ground State ◽  
Loop Model ◽  
Plane Partitions

We prove the Razumov–Stroganov conjecture relating ground state of the $O(1)$ loop model and counting of Fully Packed Loops in the case of certain types of link patterns. The main focus is on link patterns with three series of nested arches, for which we use as key ingredient of the proof a generalization of the MacMahon formula for the number of plane partitions which includes three series of parameters.

scholarly journals The Toggle Group, Homomesy, and the Razumov-Stroganov Correspondence

10.37236/5158 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Jessica Striker
Keyword(s):  
Ground State ◽  
Statistical Physics ◽  
Infinite Cylinder ◽  
Loop Model ◽  
Alternating Sign Matrices ◽  
Important Link

The Razumov-Stroganov correspondence, an important link between statistical physics and combinatorics proved in 2011 by L. Cantini and A. Sportiello, relates the ground state eigenvector of the $O(1)$ dense loop model on a semi-infinite cylinder to a refined enumeration of fully-packed loops, which are in bijection with alternating sign matrices. This paper reformulates a key component of this proof in terms of posets, the toggle group, and homomesy, and proves two new homomesy results on general posets which we hope will have broader implications.

scholarly journals Exact expressions for correlations in the ground state of the dense O(1) loop model

2004 ◽  
Vol 2004 (09) ◽  
pp. P09010 ◽  
Author(s):  
S Mitra ◽  
B Nienhuis ◽  
J de Gier ◽  
M T Batchelor
Keyword(s):  
Ground State ◽  
Loop Model

scholarly journals On some ground state components of the O(1) loop model

2009 ◽  
Vol 2009 (03) ◽  
pp. P03025 ◽  
Author(s):  
Tiago Fonseca ◽  
Paul Zinn-Justin
Keyword(s):  
Ground State ◽  
Loop Model

Renilla Bioluminescence: A Morphologic Approach to the Location of Photocytes

1974 ◽  
Vol 32 ◽  
pp. 208-209
Author(s):  
Ben O. Spurlock ◽  
Milton J. Cormier
Keyword(s):  
Excited State ◽  
Ground State ◽  
Molecular Basis ◽  
Light Emission ◽  
Chemical Basis ◽  
Electronic Excited State ◽  
Colonial Form ◽  
The Common ◽  
Eighteenth And Nineteenth Centuries ◽  
Catalyzed Oxidation

The phenomenon of bioluminescence has fascinated layman and scientist alike for many centuries. During the eighteenth and nineteenth centuries a number of observations were reported on the physiology of bioluminescence in Renilla, the common sea pansy. More recently biochemists have directed their attention to the molecular basis of luminosity in this colonial form. These studies have centered primarily on defining the chemical basis for bioluminescence and its control. It is now established that bioluminescence in Renilla arises due to the luciferase-catalyzed oxidation of luciferin. This results in the creation of a product (oxyluciferin) in an electronic excited state. The transition of oxyluciferin from its excited state to the ground state leads to light emission.

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