Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals

• A numerical characterization is given of the h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree <= d and shifted pure. (d - 1)-dimensional simplicial complexes.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Simplicial complex

face numbers

Stanley-Reisner rings

sequential Cohen-Macaulayness

componentwise linear ideals

Publication and Content Type

ref (subject category)

art (subject category)