RT Dissertation/Thesis
T1 Some results and Algorithms on matroids, simplicial complexes and Alexandroff spaces
A1 Nawaf Aldeifi, Sahar
K1 Simplicial complex
K1 Alexandroff spaces
K1 combinatorial homotopy
K1 matroids
AB In 1950 when JHC Whitehead introduced the idea of elementary collapse ofsimplicial complexes and the simple homotopy type.In 2012 Barmar and Minian return to the topic and develop the theory of strong collapse of simplicial complexes,which has interesting applications to collapsibility problems.In this thesis we first review both concepts and a third one - edge contraction- and explore their consequences onmatroids (a special kind of simplicial complexes). Secondly, we study a generalization of the idea of strong collapseto (non-finite) Alexandroff spaces. Finally, we present several algorithms to facilitate the exploration of all theseconcepts in the case of finite simplicial complexes and directed graphs.
YR 2022
FD 2022
LK http://hdl.handle.net/10347/29345
UL http://hdl.handle.net/10347/29345
LA eng
DS Minerva
RD 29 abr 2026