Geodesic
Semifinite harmonic functions on the direct product of graded graphs
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 125-150

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Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained. 
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     author = {P. Nikitin and N. Safonkin},
     title = {Semifinite harmonic functions on the direct product of graded graphs},
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P. Nikitin; N. Safonkin. Semifinite harmonic functions on the direct product of graded graphs. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 125-150. http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a7/