2016
DOI: 10.1142/s0218216516420037
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Manifolds associated to simple games

Abstract: Abstract. Starting by a simple game Q as a combinatorial data, we build up a cell complex M (Q), whose construction resembles combinatorics of the permutohedron. The cell complex proves to be a combinatorial manifold; we call it the simple game induced manifold. By some motivations coming from polygonal linkages, we think of Q and of M (Q) as of a quasilinkage and the moduli space of the quasilinkage respectively. We present some examples of quasilinkages and show that the moduli space retains many properties … Show more

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Cited by 8 publications
(8 citation statements)
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“…In turn, these are defined by the collection of short sets. This suggests the following generalization, which is described in details in [2], and which we sketch very briefly now. The proposed notion exists in the literature; yet in completely different frameworks.…”
Section: D+3mentioning
confidence: 98%
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“…In turn, these are defined by the collection of short sets. This suggests the following generalization, which is described in details in [2], and which we sketch very briefly now. The proposed notion exists in the literature; yet in completely different frameworks.…”
Section: D+3mentioning
confidence: 98%
“…The realization is related to cyclopermutohedron [12], which is a polytope that encodes cyclically ordered partitions of a finite set in the same way as the permutohedron encodes linearly ordered partitions. Section 4 sketches the main result of [2]: under a proper setting, a "polygonal linkage" can be replaced by a "simple game" (in the game-theoretic sense). A simple game cannot be interpreted as a physical object (like bar-and-joint mechanism) and therefore has no "configurations".…”
Section: Preliminaries and Notationmentioning
confidence: 99%
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