Graded posets inverse zeta matrix formula

Details Graded posets inverse zeta matrix formula Graded posets inverse zeta matrix formula

2009-03-14

arxiv.org/abs/0903.2575v3

Bull. Soc. Sci. Lett. Lodz . Ser. Rech. Deform. vol 60 No3 (2010): 117--147

Mathematics

Combinatorics

48 pages, 7 figures, affiliated to The Internet Gian-Carlo Polish Seminar: http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

Scientific paper

We derive the explicit formula for the inverse of zeta matrix for any graded posets with the finite set of minimal elements . The combinatorial interpretation of this result is given. For that to do special number theoretic code triangles for graded posets are proposed and apart from the present author combinatorial interpretation of $F-nomial$ coefficients another one is proposed referring to the number of all maximal chains in the corresponding poset intervals.

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