Geodesic
Extendable shellability for \(d\)-dimensional complexes on \(d+3\) vertices
Jared Culbertson1 ; Anton Dochtermann2 ; Dan P. Guralnik3 ; Peter F. Stiller4
1Air Force Research Laboratory
2University of Texas at Austin
3University of Florida
4Texas A&M University
The electronic journal of combinatorics, Tome 27 (2020) no. 3
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We prove that for all $d \geq 1$, a shellable $d$-dimensional complex with at most $d+3$ vertices is extendably shellable. The proof involves considering the structure of `exposed' edges in chordal graphs as well as a connection to linear quotients of quadratic monomial ideals.
DOI : 10.37236/9120
Classification : 05E45, 52B22, 13D02, 13F55

Jared Culbertson  1   ; Anton Dochtermann  2   ; Dan P. Guralnik  3   ; Peter F. Stiller  4

1 Air Force Research Laboratory
2 University of Texas at Austin
3 University of Florida
4 Texas A&M University 
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     author = {Jared Culbertson and Anton Dochtermann and Dan P. Guralnik and Peter F. Stiller},
     title = {Extendable shellability for \(d\)-dimensional complexes on \(d+3\) vertices},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {3},
     doi = {10.37236/9120},
     zbl = {1441.05251},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9120/}
}
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Jared Culbertson; Anton Dochtermann; Dan P. Guralnik; Peter F. Stiller. Extendable shellability for \(d\)-dimensional complexes on \(d+3\) vertices. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/9120

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