betti C
The diagram can be used to determine the degrees of the entries in the matrices of the differentials in a chain complex (which is a type of graded module) provided they are homogeneous maps of degree 0.
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Column j of the top row of the diagram gives the rank of the free module C_j. The entry in column j in the row labelled i is the number of basis elements of (weighted) degree i+j in the free module C_j. When the chain complex is the resolution of a module the entries are the total and the graded Betti numbers of the module.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/OldChainComplexes/docs/betti-doc.m2:108:0.