Block inclusions and cores of partitions

Spin block inclusions

In this paper we classify all block equalities and all nontrivial block inclusions for spin blocks of the double covers of the symmetric groups at different odd primes. More generally, we describe for an odd integer s > 1 explicitly when an s̄-block of bar partitions is contained in a t̄-block of bar partitions, for t > 1 an odd integer or t = 4. The question of block equality leads to the study ...

Differential transformation method for solving fuzzy differential inclusions by fuzzy partitions

A theorem on the cores of partitions

Suppose that s, t ∈ N are relatively prime positive integers. In the study of block inclusions between sand t-blocks of partitions [4] we introduced an (s, t)-abacus to study relations between sand t-cores of partitions. This is because the cores determine the blocks. Before we state our main result let us mention that the basic facts about partitions, hooks and blocks of partitions may be foun...

Core partitions and block coverings

A number of new results about core partitions have been proved recently. ([2],[3], [9], [12]) For s ∈ N an s-core is by definition an integer partition without hooks of length s. This type of partitions first occurred in modular representation theory of symmetric groups, where s-cores label s-blocks of defect 0 in the case where s is a prime. In the study of relations between blocks for differe...

Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...