Geodesic
A~cohomological characteristic for the length and width of a~partially ordered set
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 217-227

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Grothendieck topologies on a poset preset by one set and corresponding sheaf cohomologies are analyzed. The relation between the given cohomologies and the length of a poset is identified. For this purpose, Grothendieck topologies are defined on the set of the chains and antichains of the given poset; the corresponding theories of sheaf cohomologies are formed and with the help of those the poset is analyzed. 
@article{FPM_2009_15_7_a10,
     author = {A. G. Sukhonos},
     title = {A~cohomological characteristic for the length and width of a~partially ordered set},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {217--227},
     publisher = {mathdoc},
     volume = {15},
     number = {7},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_7_a10/}
}
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A. G. Sukhonos. A~cohomological characteristic for the length and width of a~partially ordered set. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 217-227. http://geodesic.mathdoc.fr/item/FPM_2009_15_7_a10/