scholarly journals From Flag Complexes to Banner Complexes

2013 ◽  
Vol 27 (2) ◽  
pp. 1146-1158 ◽  
Author(s):  
Steven Klee ◽  
Isabella Novik
Keyword(s):  
Flag Complexes

scholarly journals Cohen–Macaulay Graphs and Face Vectors of Flag Complexes

2012 ◽  
Vol 26 (1) ◽  
pp. 89-101 ◽  
Author(s):  
David Cook ◽  
Uwe Nagel
Keyword(s):  
Face Vectors ◽  
Flag Complexes

scholarly journals Face vectors of flag complexes

2008 ◽  
Vol 164 (1) ◽  
pp. 153-164 ◽  
Author(s):  
Andrew Frohmader
Keyword(s):  
Face Vectors ◽  
Flag Complexes

scholarly journals Simplicial Complexes are Game Complexes

10.37236/6958 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Sara Faridi ◽  
Svenja Huntemann ◽  
Richard J. Nowakowski
Keyword(s):  
Simplicial Complex ◽  
Simplicial Complexes ◽  
Combinatorial Games ◽  
Natural Question ◽  
Flag Complex ◽  
Game Trees ◽  
Game Value ◽  
Flag Complexes

Strong placement games (SP-games) are a class of combinatorial games whose structure allows one to describe the game via simplicial complexes. A natural question is whether well-known parameters of combinatorial games, such as "game value", appear as invariants of the simplicial complexes. This paper is the first step in that direction. We show that every simplicial complex encodes a certain type of SP-game (called an "invariant SP-game") whose ruleset is independent of the board it is played on. We also show that in the class of SP-games isomorphic simplicial complexes correspond to isomorphic game trees, and hence equal game values. We also study a subclass of SP-games corresponding to flag complexes, showing that there is always a game whose corresponding complex is a flag complex no matter which board it is played on.

scholarly journals On Lusztig-Dupont homology of flag complexes

2019 ◽  
Vol 531 ◽  
pp. 83-101
Author(s):  
Roy Meshulam ◽  
Shira Zerbib
Keyword(s):  
Flag Complexes

scholarly journals The homotopy theory of polyhedral products associated with flag complexes

2018 ◽  
Vol 155 (1) ◽  
pp. 206-228
Author(s):  
Taras Panov ◽  
Stephen Theriault
Keyword(s):  
Simplicial Complex ◽  
Homotopy Theory ◽  
Chordal Graph ◽  
Polyhedral Product ◽  
Flag Complex ◽  
Vertex Set ◽  
Flag Complexes

If $K$ is a simplicial complex on $m$ vertices, the flagification of $K$ is the minimal flag complex $K^{f}$ on the same vertex set that contains $K$. Letting $L$ be the set of vertices, there is a sequence of simplicial inclusions $L\stackrel{}{\longrightarrow }K\stackrel{}{\longrightarrow }K^{f}$. This induces a sequence of maps of polyhedral products $(\text{}\underline{X},\text{}\underline{A})^{L}\stackrel{g}{\longrightarrow }(\text{}\underline{X},\text{}\underline{A})^{K}\stackrel{f}{\longrightarrow }(\text{}\underline{X},\text{}\underline{A})^{K^{f}}$. We show that $\unicode[STIX]{x1D6FA}f$ and $\unicode[STIX]{x1D6FA}f\circ \unicode[STIX]{x1D6FA}g$ have right homotopy inverses and draw consequences. For a flag complex $K$ the polyhedral product of the form $(\text{}\underline{CY},\text{}\underline{Y})^{K}$ is a co-$H$-space if and only if the 1-skeleton of $K$ is a chordal graph, and we deduce that the maps $f$ and $f\circ g$ have right homotopy inverses in this case.

scholarly journals Face Numbers of Certain Cohen–Macaulay Flag Complexes

2011 ◽  
Vol 25 (4) ◽  
pp. 1768-1777 ◽  
Author(s):  
Jonathan Browder
Keyword(s):  
Flag Complexes

scholarly journals A class of hypergraphs that generalizes chordal graphs

2010 ◽  
Vol 106 (1) ◽  
pp. 50 ◽  
Author(s):  
Eric Emtander
Keyword(s):  
Simplicial Complexes ◽  
Natural Generalization ◽  
Chordal Graphs ◽  
Graph Algebras ◽  
Higher Dimensional ◽  
Dimensional Version ◽  
Definition Of ◽  
Flag Complexes ◽  
Circuit Graph

In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given by H. T. Hà and A. Van Tuyl, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal (rigid circuit) graph. R. Fröberg has showed that the chordal graphs corresponds to graph algebras, $R/I(\mathcal{G})$, with linear resolutions. We extend Fröberg's method and show that the hypergraph algebras of generalized chordal hypergraphs, a class of hypergraphs that includes the chordal hypergraphs, have linear resolutions. The definitions we give, yield a natural higher dimensional version of the well known flag property of simplicial complexes. We obtain what we call $d$-flag complexes.

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