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Enumeration of idempotents in diagram semigroups and algebras
TLDR
We give a characterisation of the idempotents of the partition monoid, and use this to enumerate the number of idemptents in the finite partition, Brauer and partial Brauer monoids, giving several formulae and recursions. Expand
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Classifications of Symmetric Normal Form Games
  • Nicholas Ham
  • Mathematics, Computer Science
  • ArXiv
  • 18 November 2013
TLDR
In this paper we survey various classifications of symmetric games and their characterisations under the theme of fairness; show that game bijections and game isomorphisms form groupoids; introduce matchings as a convenient characterisation of strategy triviality; and outline how to construct and partially order parameterised asymmetric games with numerous examples that range over various classes. Expand
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Enumeration of idempotents in planar diagram monoids
We classify and enumerate the idempotents in several planar diagram monoids: namely, the Motzkin, Jones (a.k.a. Temperley-Lieb) and Kauffman monoids. The classification is in terms of certain vertex-Expand
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Idempotent Statistics of the Motzkin and Jones Monoids
We describe a refinement of the natural partial order on the set of idempotents of the Motzkin monoid of general degree n which exhibits its structure as a disjoint union of geometric complexes. ThisExpand
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Notions of Symmetry for Finite Strategic-Form Games
In this paper we survey various notions of symmetry for finite strategic-form games; show that game bijections and game isomorphisms form groupoids; introduce matchings as a convenientExpand
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Some Structure Properties of Finite Normal-Form Games
TLDR
Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Expand
1 Permutations Acting On Strategy Profiles
In this paper we survey various notions of symmetry for finite strategic-form games; show that game bijections and game isomorphisms form groupoids; introduce matchings as a convenientExpand
Notions of Anonymity, Fairness and Symmetry for Finite Strategic-Form Games
In this paper we survey the various notions of anonymity and symmetry for finite strategic-form games that are present in the literature, and discuss notions of fairness; show that game bijectionsExpand
Semigroups: 2.8.0
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Lattice paths and submonoids of $\mathbb Z^2$.
We study a number of combinatorial and algebraic structures arising from walks on the two-dimensional integer lattice. To a given step set $X\subseteq\mathbb Z^2$, there are two naturally associatedExpand
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