Partial Algebraic Shifting Article Swipe
Related Concepts
Algebraic number
Mathematics
Algebra over a field
Pure mathematics
Mathematical analysis
A. Della Vecchia
,
Michael Joswig
,
Fabian Lenzen
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2410.24044
· OA: W4404347955
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2410.24044
· OA: W4404347955
We study algebraic shifting of uniform hypergraphs and finite simplicial complexes in the exterior algebra with respect to matrices which are not necessarily generic. Several questions raised by Kalai (2002) are addressed. For instance, it turns out that the combinatorial shifting of Erdős$\unicode{x2013}$Ko$\unicode{x2013}$Rado (1961) arises as a special case. Moreover, we identify a sufficient condition for partial shifting to preserve the Betti numbers of a simplicial complex; examples show that this condition is sharp.
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