Abstract
A multicomplexM is a collection of monomials closed under divisibility. For suchM we construct a cell complex ΔM 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 ΔM. For squarefree monomials the construction specializes to the standard geometric realization of a simplicial complex.
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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.