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I am looking for the technical term for an element of a transformation semigroup that sends everything to one state. The best term I could think up was filter.

For those that don't know a trasformation is like a permutation, except you can have repeated entries.

Identity permutation/transformation

[1,2,3,4] [1->1, 2->2, 3->3, 4 ->4]

Legal permutation/transformation

[2,1,4,3] [1->2, 2->1, 3->4, 4->3]

Illegal permutation, legal transformation:

[1,1,3,4] [1->1, 2->1, 3->3, 4->4]

Transformations I would like to know the technical term for:

[1,1,1,1]

[2,2,2,2]

[3,3,3,3]

[4,4,4,4]

  • 0
    what about "constant transformation"?2012-10-10

1 Answers 1

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The correct term is constant transformation; see http://www.m-hikari.com/ija/ija-2011/ija-29-32-2011/kelekciIJA29-32-2011.pdf.

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    In automata theory the word "reset" is also used and a word in the generators which represents a constant transformation is often called a synchronizing word or reset word.2013-09-11