Geodesic
A combinatorial formula for monomials in Kontsevich's $\psi$-classes
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 485 (2019), pp. 72-77

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Diagonal complexes provide a simplicial model for the Kontsevich's tautological bundles over $\mathcal{M}_{g,n}$. Local combinatorial formula for the first Chern class yields a combinatorial formula for the $\psi$-classes (that is, first Chern classes of the tautological bundles). In the present paper we derive a formula for arbitrary monomials in $\psi$-classes. 
@article{ZNSL_2019_485_a3,
     author = {J. Gordon and G. Panina},
     title = {A combinatorial formula for monomials in {Kontsevich's} $\psi$-classes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {72--77},
     publisher = {mathdoc},
     volume = {485},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_485_a3/}
}
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J. Gordon; G. Panina. A combinatorial formula for monomials in Kontsevich's $\psi$-classes. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 485 (2019), pp. 72-77. http://geodesic.mathdoc.fr/item/ZNSL_2019_485_a3/