Geodesic
Combinatorics of a statistical model constructed from the $2\times n$ square lattice
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 72-78

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Various weight functions for the model of a $2\times n$ square lattice are defined so that the graded Euler characteristic for the complex corresponding to this model remain equal to the usual one. Differentials preserving these gradings and determining one-dimensional cohomology are also specified.
Keywords: hard-square model, square ladder, Euler characteristic, grading, weight function, square lattice. 
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     author = {B. L. Feigin and V. V. Sopin},
     title = {Combinatorics of a statistical model constructed from the $2\times n$ square lattice},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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B. L. Feigin; V. V. Sopin. Combinatorics of a statistical model constructed from the $2\times n$ square lattice. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 72-78. http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a6/