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 Fundam. Prikl. Mat., 2009, Volume 15, Issue 7, Pages 217–227 (Mi fpm1279)

A cohomological characteristic for the length and width of a partially ordered set

A. G. Sukhonos

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: 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.

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English version:
Journal of Mathematical Sciences (New York), 2010, 169:5, 705–712

Bibliographic databases:

UDC: 512.667+512.667.5+512.562

Citation: A. G. Sukhonos, “A cohomological characteristic for the length and width of a partially ordered set”, Fundam. Prikl. Mat., 15:7 (2009), 217–227; J. Math. Sci., 169:5 (2010), 705–712

Citation in format AMSBIB
\Bibitem{Suk09} \by A.~G.~Sukhonos \paper A~cohomological characteristic for the length and width of a~partially ordered set \jour Fundam. Prikl. Mat. \yr 2009 \vol 15 \issue 7 \pages 217--227 \mathnet{http://mi.mathnet.ru/fpm1279} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2745011} \transl \jour J. Math. Sci. \yr 2010 \vol 169 \issue 5 \pages 705--712 \crossref{https://doi.org/10.1007/s10958-010-0071-2} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77956059374}