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First we recall homology groups of prer Lie superalgebras. Then introducingdouble weighted chain spaces, we deal with pre Lie superalgebra of multi-vectorfields with polynomial coefficients on n-dimensional number space. The bracketis Schouten bracket. We have several results about Euler number and Bettinumbers of those homology groups of special pre Lie superalgebra.

Euler number and Betti numbers of homology groups of pre Lie superalgebra