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Abstract: Given a positive integer n and a finite alphabet A, a word w over A is said to guarantee minimal image if, for every homomorphism ' from the free monoid A over A into the monoid of all transformations of an n-element set, the range of the transformation w' has the minimum cardinality among the ranges of all transformations of the form v' where v runs over A . Although the existence of words guaranteeing minimal image is pretty obvious, the problem of their explicit description is very far from... (Update)
Context of citations to this paper: More
...equivalent to constructing a sequence of words guaranteeing 9 minimum image in each nite full transformation semigroup. We refer to [24] for several explicit constructions of word sequences with the latter property: these constructions are based on an interesting interplay...
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BibTeX entry: (Update)
S. Margolis, J.-E. Pin and M. V. Volkov, Words guaranteeing minimal image, submitted. http://citeseer.ist.psu.edu/593505.html More
@misc{ margolis-words,
author = "S. Margolis and J. Pin and M. Volkov",
title = "Words guaranteeing minimal image",
text = "S. Margolis, J.-E. Pin and M. V. Volkov, Words guaranteeing minimal image,
submitted.",
url = "citeseer.ist.psu.edu/593505.html" }
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