Onf-vectors and Betti numbers of multicomplexes |
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Authors: | Anders Björner Siniša Vrećica |
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Institution: | (1) Matematiska Institutionen, Kungliga Tekniska Högskolan, S-100 44 Stockholm, Sweden;(2) Faculty of Mathematics, University of Belgrade, 11001 Belgrade, Yugoslavia |
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Abstract: | A multicomplexM is a collection of monomials closed under divisibility. For suchM we construct a cell complex M whosei-dimensional cells are in bijection with thef
i
monomials ofM of degreei+1. The bijection is such that the inclusion relation of cells corresponds to divisibility of monomials. We then study relations between the numbersf
i
and the Betti numbers of M. For squarefree monomials the construction specializes to the standard geometric realization of a simplicial complex.This work was supported by the Mittag-Leffler Institute during the Combinatorial Year program 1991–92. The second author also acknowledges support from the Serbian Science Foundation, Grant No. 0401D. |
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Keywords: | 05 E 99 55 M 99 05 D 05 55 N 99 |
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