scholarly journals Stanley–Reisner rings for symmetric simplicial complexes, $G$-semimatroids and Abelian arrangements

2021 ◽  
Vol 5 (3) ◽  
pp. 185-236
Author(s):  
Alessio D’Alì ◽  
Emanuele Delucchi
Keyword(s):  
Simplicial Complexes

Algebraic Shifting and Sequentially Cohen-Macaulay Simplicial Complexes

10.37236/1245 ◽  
1996 ◽  
Vol 3 (1) ◽  
Author(s):  
Art M. Duval
Keyword(s):  
Simplicial Complex ◽  
Simplicial Complexes ◽  
Pure Case ◽  
Definition Of ◽  
Algebraic Shifting

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the $h$-triangle, a doubly-indexed generalization of the $h$-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generalize the Cohen-Macaulay conditions for pure complexes, so that a nonpure shellable complex is sequentially Cohen-Macaulay. We show that algebraic shifting preserves the $h$-triangle of a simplicial complex $K$ if and only if $K$ is sequentially Cohen-Macaulay. This generalizes a result of Kalai's for the pure case. Immediate consequences include that nonpure shellable complexes and sequentially Cohen-Macaulay complexes have the same set of possible $h$-triangles.

scholarly journals Constructing selections stepwise over cones of simplicial complexes

2020 ◽  
Vol 275 ◽  
pp. 107032
Author(s):  
Valentin Gutev
Keyword(s):  
Simplicial Complexes

scholarly journals The Stellar decomposition: A compact representation for simplicial complexes and beyond

2021 ◽  
Author(s):  
Riccardo Fellegara ◽  
Kenneth Weiss ◽  
Leila De Floriani
Keyword(s):  
Simplicial Complexes ◽  
Compact Representation

scholarly journals Homological percolation transitions in growing simplicial complexes

2021 ◽  
Vol 31 (4) ◽  
pp. 041102
Author(s):  
Y. Lee ◽  
J. Lee ◽  
S. M. Oh ◽  
D. Lee ◽  
B. Kahng
Keyword(s):  
Simplicial Complexes

scholarly journals Algebraic and combinatorial expansion in random simplicial complexes

2021 ◽  
Author(s):  
Nikolaos Fountoulakis ◽  
Michał Przykucki
Keyword(s):  
Simplicial Complexes ◽  
Random Simplicial Complexes

scholarly journals A simplification of the Eilenberg-Steenrod axioms for finite simplicial complexes

1988 ◽  
Vol 53 (3) ◽  
pp. 257-265 ◽  
Author(s):  
Robert J.MacG. Dawson
Keyword(s):  
Simplicial Complexes

scholarly journals The extremal symmetry of arithmetic simplicial complexes

2012 ◽  
Vol 231 (2) ◽  
pp. 843-854
Author(s):  
Benson Farb ◽  
Amir Mohammadi
Keyword(s):  
Simplicial Complexes

Linear codes from simplicial complexes

2017 ◽  
Vol 86 (10) ◽  
pp. 2167-2181 ◽  
Author(s):  
Seunghwan Chang ◽  
Jong Yoon Hyun
Keyword(s):  
Linear Codes ◽  
Simplicial Complexes

scholarly journals Weighted growing simplicial complexes

2017 ◽  
Vol 95 (6) ◽  
Author(s):  
Owen T. Courtney ◽  
Ginestra Bianconi
Keyword(s):  
Simplicial Complexes
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