Geodesic
The singularity of some relations and their combinatorial applications
Diskretnaya Matematika, Tome 8 (1996) no. 2, pp. 63-88.

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We give the conditions of reversibility of the zeta function and formulae for computing the Möbius functions of the join relation, disjoint relation, cover relation, and complement relation. Many combinatorial assertions are obtained as corollaries of non-singularity of these relations. 
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     author = {E. E. Marenich},
     title = {The singularity of some relations and their combinatorial applications},
     journal = {Diskretnaya Matematika},
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     volume = {8},
     number = {2},
     year = {1996},
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     url = {http://geodesic.mathdoc.fr/item/DM_1996_8_2_a4/}
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E. E. Marenich. The singularity of some relations and their combinatorial applications. Diskretnaya Matematika, Tome 8 (1996) no. 2, pp. 63-88. http://geodesic.mathdoc.fr/item/DM_1996_8_2_a4/