Chapter 11 offers a self-contained and systematic presentation of modern shifting theory from the viewpoint of generic initial ideals as well as of graded Betti numbers. Combinatorial, exterior and symmetric shifting are introduced and the comparison of the graded Betti numbers for the distinct shifting operators is studied. It is shown that the extremal graded Betti numbers of a simplicial complex and its symmetric and exterior shifted complex are the same. Finally, super-extremal Betti numbers are considered to give an algebraic proof of the Björner–Kalai theorem.
KeywordsExact Sequence Simplicial Complex Betti Number Hilbert Function Monomial Ideal
Unable to display preview. Download preview PDF.