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In 1998, the second author raised the problem of classifying the irreducible characters of S n of prime power degree. Zalesskii proposed the analogous problem for quasi-simple groups, and he has, in joint work with Malle, made substantial progress on this latter problem. With the exception of the alternating groups and their double covers, their work… (More)
Recently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisym-metric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur… (More)
In this paper we study the homogeneous tensor products of simple modules over symmetric and alternating groups.
The well-known fact that there is always one more addable than removable box for a Young diagram is generalized to arbitrary hooks. As an application, this implies immediately a simple proof of a conjecture of Regev and Vershik 3] for which inductive proofs have recently been given by Regev and Zeilberger 4] and Janson 1].
We present a general construction of involutions on integer partitions which enable us to prove a number of modulo 2 partition congru-ences.
There is a simple formula for the absolute value of the determinant of the character table of the symmetric group S n. It equals a P , the product of all parts of all partitions of n (see [4, Corollary 6.5]). In this paper we calculate the absolute values of the determinants of certain submatrices of the character table X of the alternating group A n ,… (More)
Extending the partition function multiplicatively to a function on partitions, we show that it has a unique maximum at an explicitly given partition for any n = 7. The basis for this is an inequality for the partition function which seems not to have been noticed before.