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Almost associative operations generating a minimal clone

100%

Waldhauser T.

Discussiones Mathematicae - General Algebra and Applications

2006

tom 26

nr 1

45-73

Characterizations of 'almost associative' binary operations generating a minimal clone are given for two interpretations of the term 'almost associative'. One of them uses the associative spectrum, the other one uses the index of nonassociativity to measure how far an operation is from being associative.

Invariance groups of finite functions and orbit equivalence of permutation groups

51%

Horváth E. K., Makay G., Pöschel R., Waldhauser T.

Open Mathematics

2015

tom 13

nr 1

Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections and the corresponding closure operators on Sn, which turn out to provide a generalization of orbit equivalence of permutation groups. We also present some computational results, which show that all primitive groups except for the alternating groups arise as invariance groups of functions defined on a three-element domain.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Open Mathematics

2 Waldhauser T.

1 Horváth E. K.

1 Makay G.

1 Pöschel R.

1 2015

1 2006

Wyniki wyszukiwania

Almost associative operations generating a minimal clone

Invariance groups of finite functions and orbit equivalence of permutation groups