Anne Fearnley

Champs d'intérêts Algèbre universelle: théorie des clones Clones sur un nombre fini d'éléments Intervalles monoïdaux Fonctions préservant des relations

Research Interests Universal Algebra: clone theory Clones on a finite number of elements Monoidal intervals Functions preserving relations

Publications

• FEARNLEY, Anne, The monoidal interval for the monoid generated by two constants, Accepted by the Journal of Multiple-Valued Logic and Soft Computing. PDF
  Abstract: Post (1941) presented the complete description of the countably many clones on 2 elements. The structure of the lattice of clones on finitely many (but more than 2) elements is more complex; in fact, the lattice is of cardinality $2^{\aleph_0}$. One approach is to study the monoidal intervals: the set of clones whose unary operations form a given monoid. In this article, we study the monoidal interval for the monoid generated by two constants on k elements for k finite. This interval contains the clones of term operations of the bounded lattices of k elements.
  
  
• FEARNLEY, Anne, The clone of operations preserving a cycle with loops, Algebra Universalis, 60, pp. 91-106, 2009. PDF
  Abstract: We consider all the binary relations on $k$-elements which, when viewed as directed graphs, consist of a $k$-cycle and some loops. If $k \geq 3$ and the relation has at least 2 loops, we show that it is only preserved by essentially unary operations. In all other cases, the relation preserves operations that depend on a greater number of variables.
  The original publication is available at www.springerlink.com.
  
  
• FEARNLEY, Anne, Clones on three elements preserving a binary relation, Algebra Universalis, 56, pp. 165-177, 2007. PDF
  Abstract: We describe the clones on 3 elements that can be expressed as Pol r for r a binary relation. We present the poset of these clones ordered by inclusion. This article is a shortened version to give an idea of the whole work.
  The original publication is available at www.springerlink.com.
  
  
• FEARNLEY, Anne & ROSENBERG, Ivo, Collapsing monoids containing permutations and constants, Algebra Universalis, 50, pp. 149-156, 2003. PDF
  Abstract: In 1941, Post presented the complete description of the countably many clones on 2 elements. The structure of the lattice of clones on finitely many (but more than 2) elements is more complex; in fact the lattice is of cardinality $2^{\aleph_0}$. One approach is to study the monoidal intervals: the set of clones whose unary operations form a given monoid. One surprising fact is that for certain monoids, called collapsing, this interval contains just one clone. This article presents some collapsing monoids containing only constants and permutations.
  The original publication is available at www.springerlink.com.
  
  
• FEARNLEY, Anne, A strongly rigid binary relation, Acta Sci. Math. (Szeged), 61, pp. 35-41, 1995. PDF
  Abstract: A binary relation r on a set U is strongly rigid if every universal algebra on U such that r is a subuniverse of its square is trivial. Rosenberg (1973) found a strongly rigid relation on every universe U of at least 3 elements. We exhibit a new strongly rigid relation for every finite U of cardinality at least 3. We also show that, if U contains only 3 elements, there are only 2 strongly rigid relations up to isomorphism.
  
  

Autres écrits / Other writings

• FEARNLEY, Anne, Clones de constantes et de permutations et leur intervalle monoïdal, thèse de doctorat / PhD thesis. PDF
  
  
• FEARNLEY, Anne, Clones on three elements preserving a binary relation, manuscript. PDF
  Abstract: We describe the clones on 3 elements that can be expressed as Pol r for r a binary relation. We present the poset of these clones ordered by inclusion. This is essentially my Master's thesis with a few improvements and a new theorem. It is the complete version of the article that was published in Algebra Universalis.
  
  
• FEARNLEY, Anne, Post's Lattice, manuscript PDF - LaTeX
  Abstract: A drawing of the lattice of clones on 2 elements using Post's notation. A description of the clones and several other useful information about clones on 2 elements.