scholarly journals Intermediate symplectic characters and shifted plane partitions of shifted double staircase shape

2021 ◽  
Vol 1 (0) ◽  
Author(s):  
Soichi Okada
Keyword(s):  
Plane Partitions ◽  
Symplectic Characters

scholarly journals Plane partitions of shifted double staircase shape

2021 ◽  
Vol 183 ◽  
pp. 105486
Author(s):  
Sam Hopkins ◽  
Tri Lai
Keyword(s):  
Plane Partitions

scholarly journals Resonance in orbits of plane partitions and increasing tableaux

2017 ◽  
Vol 148 ◽  
pp. 244-274 ◽  
Author(s):  
Kevin Dilks ◽  
Oliver Pechenik ◽  
Jessica Striker
Keyword(s):  
Plane Partitions

scholarly journals Notes on plane partitions. II

1968 ◽  
Vol 4 (1) ◽  
pp. 81-99 ◽  
Author(s):  
Basil Gordon ◽  
Lorne Houten
Keyword(s):  
Plane Partitions

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 An Orthosymplectic Pieri Rule

10.37236/7387 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Anna Stokke
Keyword(s):  
Linear Combination ◽  
Schur Functions ◽  
Symmetric Polynomial ◽  
Schur Function ◽  
Product Rule ◽  
Integer Coefficients ◽  
Pieri Formula ◽  
Symplectic Characters ◽  
Homogeneous Symmetric Polynomial

The classical Pieri formula gives a combinatorial rule for decomposing the product of a Schur function and a complete homogeneous symmetric polynomial as a linear combination of Schur functions with integer coefficients. We give a Pieri rule for describing the product of an orthosymplectic character and an orthosymplectic character arising from a one-row partition. We establish that the orthosymplectic Pieri rule coincides with Sundaram's Pieri rule for symplectic characters and that orthosymplectic characters and symplectic characters obey the same product rule. 

scholarly journals Correlation functions for a strongly coupled boson system and plane partitions

2011 ◽  
Vol 369 (1939) ◽  
pp. 1319-1333 ◽  
Author(s):  
Nikolay Bogoliubov ◽  
Jussi Timonen
Keyword(s):  
Correlation Functions ◽  
Finite Size ◽  
Temperature Limit ◽  
Phase Model ◽  
Strong Interactions ◽  
Scaling Exponent ◽  
Strongly Correlated ◽  
Strongly Coupled ◽  
Plane Partitions ◽  
Hopping Model

A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q -boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.

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