Results 11 to 20 of about 341 (183)
Partial Orders on Transformation Semigroups [PDF]
Monatshefte f�r Mathematik, 2003 Denote by \(P(X)\) the semigroup, under composition, of all partial transformations of the set \(X\). Denote by \(\text{dom\,}\alpha\) the domain of \(\alpha\in P(X)\) and denote its range by \(\text{ran\,}\alpha\). Define a partial order \(\leq\) on \(P(X)\) by \(\alpha\leq\beta\) if \(\alpha=\gamma\beta=\beta\mu\) and \(\alpha=\alpha\mu\) for some \(\
Smith, M. Paula Marques, Sullivan, R. P.
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Open Mathematics, 2021 Let T(X)T\left(X) be the full transformation semigroup on a set XX. For an equivalence EE on XX, let TE∗(X)={α∈T(X):∀x,y∈X,(x,y)∈E⇔(xα,yα)∈E}.{T}_{{E}^{\ast }}\left(X)=\left\{\alpha \in T\left(X):\forall x,y\in X,\left(x,y)\in E\iff \left(x\alpha ,y ...
Sangkhanan Kritsada
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Computing Transformation Semigroups
Journal of Symbolic Computation, 2002 The paper describes data structures and algorithms for performing computations in a finite semigroup \(S\) with identity, generated by a set of transformations. A basic idea behind the algorithms is the partition of \(S\) with the aid of an equivalence relation \(\mathcal R\), one of Green's relations.
Steve Linton +3 more
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On left restriction semigroups with zero
Kuwait Journal of Science, 2023 In this article, we give the notion of left restriction meet-semigroup, and establish some results regarding atomistic left restriction semigroups. Then we discuss decompositions of (non-zero) semigroups with zero by proving a decomposition theorem.
Baddi Ul Zaman
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Exploring Tetris as a Transformation Semigroup [PDF]
, 2021 Tetris is a popular puzzle video game, invented in 1984. We formulate two versions of the game as a transformation semigroup and use this formulation to view the game through the lens of Krohn-Rhodes theory. In a variation of the game upon which it restarts if the player loses, we find permutation group structures, including the symmetric group $S_5 ...
Peter C. Jentsch, Chrystopher L. Nehaniv
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Representation of right zero semigroups and their semilattices by a transformation semigroup
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. As is known, an arbitrary semigroup can be represented by a semigroup of transformations that are right shifts either in this semigroup itself or in the extended semigroup obtained from the original one by adding an outer unit. The problems
L.V. Zyablitseva +2 more
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A NEW METHOD FOR CONSTRUCTING PARTIAL ONE TO ONE TRANSFORMATION SEMIGROUP USING TWO LINE NOTATION
Academy Journal of Science and Engineering, 2022 In this paper, we provide a method of constructing finite one to one transformation semigroup from the full one to one transformation semigroup using some pattern called transitive.
Muhammad Mansur Zubairu, Bashir Ali
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Transformation Representations of Sandwich Semigroups [PDF]
Experimental Mathematics, 2018 Let $a$ be an element of a semigroup $S$. The local subsemigroup of $S$ with respect to $a$ is the subsemigroup $aSa$ of $S$. The variant of $S$ with respect to $a$ is the semigroup with underlying set $S$ and operation $\star_a$ defined by $x\star_ay=xay$ for $x,y\in S$.
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Regularity and Green's Relations on a Semigroup of Transformations with Restricted Range
International Journal of Mathematics and Mathematical Sciences, 2008 Let T(X) be the full transformation semigroup on the set X and let T(X,Y)={α∈T(X):Xα⊆Y}. Then T(X,Y) is a sub-semigroup of T(X) determined by a nonempty subset Y of X.
Jintana Sanwong, Worachead Sommanee
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On Magnifying Elements in E-Preserving Partial Transformation Semigroups
Mathematics, 2018 Let S be a semigroup. An element a of S is called a right [left] magnifying element if there exists a proper subset M of S satisfying S = M a [ S = a M ] . Let E be an equivalence relation on a nonempty set X.
Thananya Kaewnoi +2 more
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