GENERATING THE FULL TRANSFORMATION SEMIGROUP USING ORDER PRESERVING MAPPINGS
نویسندگان
چکیده
منابع مشابه
Generating the Full Transformation Semigroup Using Order Preserving Mappings
For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappingsOX on X modulo the full transformation semigroup TX . In other words, we ask what is the smallest cardinality of a set A of mappings such that 〈OX ∪A 〉 = TX . When X is countably infinite or well-ordered (of arbitrary cardinality) we show that this number is one, while when X = R (the set...
متن کاملGenerating Sets of Order Preserving Mappings
Sierpiński proved in 1935 that any countable set of mappings on an infinite set X is contained in a subsemigroup of the semigroup of all maps on X, where this subsemigroup is generated by just two mappings. Since then, it has been of interest whether the result also holds when certain restrictions are placed on the properties of the maps. In this paper we investigate the minimum number of order...
متن کاملCombinatorial Deformations of the Full Transformation Semigroup
We define two deformations of the Full Transformation Semigroup algebra. One makes the algebra “as semisimple as possible”, while another leads to an eigenvalue result involving Schur functions. Preliminaries The Full Transformation Semigroup on n letters, denoted Tn, is the semigroup of all set maps w : [n] → [n], where [n] = {1, 2, . . . , n} and the multiplication is the usual composition. S...
متن کاملA Combinatorial Property of the Full Transformation Semigroup
Let c () be the collapse of full transformation semigroup, Tn. Then the general formula to calculate the number of collapsible elements, | tα-1| 2 is derived for all n 0, which is an extension of [1] (A.O. Adeniji and S.O. Makanjuola (2008), ‘On some combinatorial results of collapse and properties of height in full transformation semigroups,’ African Journal of Computing & ICT (Journal of the...
متن کاملConformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2003
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089503001460