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.
@article{10_37236_6958,
author = {Sara Faridi and Svenja Huntemann and Richard J. Nowakowski},
title = {Simplicial complexes are game complexes},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/6958},
zbl = {1422.91158},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6958/}
}
TY - JOUR
AU - Sara Faridi
AU - Svenja Huntemann
AU - Richard J. Nowakowski
TI - Simplicial complexes are game complexes
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/6958/
DO - 10.37236/6958
ID - 10_37236_6958
ER -
%0 Journal Article
%A Sara Faridi
%A Svenja Huntemann
%A Richard J. Nowakowski
%T Simplicial complexes are game complexes
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/6958/
%R 10.37236/6958
%F 10_37236_6958
Sara Faridi; Svenja Huntemann; Richard J. Nowakowski. Simplicial complexes are game complexes. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/6958
