On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes
Abstract
Let
Δ
be a stable simplicial complex on
n
vertexes. Over an arbitrary base field
K
, the symmetric algebraic shifted complex
Δ
s
of
Δ
is defined. It is proved that the Betti numbers of the Stanley-Reisner ideals in the polynomial ring
K[
x
1
,
x
2
,...,
x
n
]
of the symmetric algebraic shifted, exterior algebraic shifted and combinatorial shifted complexes of
Δ
are equal.