Geodesic
Poincar\'e polynomial of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$ and the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2017), pp. 20-27

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We obtain a combinatorial proof that the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$ satisfies the requrrent formula for Poincare polynomials of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$. 
@article{VMUMM_2017_4_a2,
     author = {N. Ya. Amburg and E. M. Kreines and G. B. Shabat},
     title = {Poincar\'e polynomial of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$ and the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {20--27},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_4_a2/}
}
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N. Ya. Amburg; E. M. Kreines; G. B. Shabat. Poincar\'e polynomial of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$ and the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2017), pp. 20-27. http://geodesic.mathdoc.fr/item/VMUMM_2017_4_a2/