On Relative Ranks of Finite Transformation Semigroups with Restricted Range

Finite Transformation ◽

Empty Subset

The transformation semigroup with restricted range [Formula: see text] is the set of all functions from a set [Formula: see text] into a non-empty subset [Formula: see text] of [Formula: see text]. In this paper, we characterize Cayley graphs of [Formula: see text] with the connection set [Formula: see text]. Moreover, the undirected property of Cayley graphs Cay [Formula: see text] is studied.

On relative ranks of finite transformation semigroups with restricted range

Ukrains’kyi Matematychnyi Zhurnal ◽

10.37863/umzh.v73i5.288 ◽

2021 ◽

Vol 73 (5) ◽

pp. 617-626

Author(s):

I. Dimitrova ◽

J. Koppitz

Keyword(s):

Restricted Range ◽

Finite Chain ◽

Relative Rank ◽

Generating Sets ◽

UDC 512.5 We determine the relative rank of the semigroup of all transformations on a finite chain with restricted range modulo the set of all orientation-preserving transformations in Moreover, we state the relative rank of the semigroup modulo the set of all order-preserving transformations in In both cases we characterize the minimal relative generating sets.

Classical Finite Transformation Semigroups

10.1007/978-1-84800-281-4 ◽

2009 ◽

Cited By ~ 70

Author(s):

Olexandr Ganyushkin ◽

Volodymyr Mazorchuk

Keyword(s):

Magnifying Elements in Linear Transformation Semigroups with Restricted Range which Nullity or Co-Rank are Infinite

Asian-European Journal of Mathematics ◽

10.1142/s1793557122500036 ◽

2021 ◽

Author(s):

Pongsan Prakitsri

Keyword(s):

Linear Transformation ◽

Restricted Range ◽

Transformation Semigroups

Rank and idempotent rank of finite full transformation semigroups with restricted range

Semigroup Forum ◽

10.1007/s00233-013-9467-x ◽

2013 ◽

Vol 87 (1) ◽

pp. 230-242 ◽

Cited By ~ 5

Author(s):

Worachead Sommanee ◽

Jintana Sanwong

Keyword(s):

Restricted Range ◽

Full Transformation ◽

Idempotent Rank

Graphs and finite transformation semigroups

Discrete Mathematics ◽

10.1016/0012-365x(73)90029-0 ◽

1973 ◽

Vol 5 (1) ◽

pp. 87-99 ◽

Cited By ~ 1

Author(s):

Romano Scozzafava

Keyword(s):

On the determination of Green's relations in finite transformation semigroups

Journal of Symbolic Computation ◽

10.1016/s0747-7171(08)80057-0 ◽

1990 ◽

Vol 10 (5) ◽

pp. 481-498 ◽

Cited By ~ 7

Author(s):

Gerard Lallement ◽

Robert Mcfadden

Keyword(s):

Green’S Relations ◽

Green's Relations ◽

On Straight Words and Minimal Permutators in Finite Transformation Semigroups

Implementation and Application of Automata - Lecture Notes in Computer Science ◽

10.1007/978-3-642-18098-9_13 ◽

2011 ◽

pp. 115-124 ◽

Cited By ~ 1

Author(s):

Attila Egri-Nagy ◽

Chrystopher L. Nehaniv

Keyword(s):

Characterization of finite amenable transformation semigroups

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700012799 ◽

1973 ◽

Vol 15 (1) ◽

pp. 86-93 ◽

Cited By ~ 2

Author(s):

Carroll Wilde

Keyword(s):

Transformation Semigroup ◽

Sufficient Conditions ◽

Mean Value ◽

Explicit Description ◽

Shift Operators ◽

Finite Transformation ◽

Invariant Means ◽

Necessary And Sufficient

Abstract. In this paper we develop necessary and sufficient conditions for a finite transformation semigroup to have a mean value which is invariant under the induced shift operators. The structure of such transformation semigroups is described and an explicit description of all possible invariant means given.