Condensation of Symmetrized Tensor Powers
β Scribed by A.J.E. Ryba
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 343 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0747-7171
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## Abstract Let __G__ be a connected, nonbipartite vertexβtransitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product __G__ Γ __G__ are the preimages of the independent sets of maximal cardinality in __G__ under projections, then the same holds for all
We consider the asymptotics of certain symmetric k-tensors, the vector analogue of sample moments for i.i.d. random variables. The limiting distribution is operator stable as an element of the vector space of real symmetric k-tensors.
Theorem 1 [Be, Corollary 2.1]. Each permutation in the alternating group A n , n 2, is a product of two l-cycles in S n if and only if either w 3n 4 x l n or n=4 and l=2. Note. Theorem 1 implies that when n=4 every even permutation is a product of two l-cycles if and only if 2 l 4. The aim of the