Reduced Kronecker products which are multiplicity free or contain only few components

It is known that the Kronecker coefficient of three partitions is a bounded and weakly increasing sequence if one increases the first part of all three partitions. Furthermore if the first parts of partitions \lambda,\mu are big enough then the coefficients of the Kronecker product [\lambda][\mu]=\sum_\n g(\l,\m,\n)[\nu] do not depend on the first part but only on the other parts. The reduced Kronecker product [\lambda]_\bullet \star[\mu]_\bullet can be viewed (roughly) as the Kronecker product [(n-|\lambda|,\lambda)][(n-|\mu|,\m)] for n big enough. In this paper we classify the reduced Kronecker products which are multiplicity free and those which contain less than 10 components.We furthermore give general lower bounds for the number of constituents and components of a given reduced Kronecker product. We also give a lower bound for the number of pairs of components whose corresponding partitions differ by one box. Finally we argue that equality of two reduced Kronecker products is only possible in the trivial case that the factors of the product are the same.Comment: 11 pages, final version. appears in European J. Combi

Reading Penelope

One consequence of the recent infusion of newer critical approaches into the study of classical literature has been a boom in studies devoted to the figure of Penelope in the Odyssey. While certain problems concerning Penelope\u27s portrayal have always been part of the agenda for Homeric scholarship, the emergence of feminist criticism and an intensified concern with the act of interpretation have focused more and more attention on a female character who occupies a surprisingly central role in the largely male dominated genre of heroic epic and whose presentation is marked by contradictions and uncertainties that demand interpretive intervention. The question of how to read the character of Penelope has become a focal point for a series of larger issues: In what ways is a female character who comes to us mediated through the poetry of a distant and patriarchal era to be seen as representative of female experience? How should we account for textual mysteries such as those surrounding Penelope, and how can we incorporate them into our understanding of the work

Women in Groups: Aeschylus\u27s \u3cem\u3eSuppliants\u3c/em\u3e and the Female Choruses of Greek Tragedy

The disqualification of Aeschylus\u27s Suppliants as our earliest surviving tragedy has inevitably led to new understandings of the play\u27s prominent chorus. While the use of the chorus as a main character was once seen as a direct link with tragedy\u27s past and a conservative reflection of tragedy\u27s origins, that fea­ture is now as likely to be viewed as an innovation. Thus H. Friis Johansen and E. H. Whittle, authors of the extensive 1980 commentary on the play, see the Suppliants as a grandiose experiment with a group instead of a single person as the main carrier of the action. In their view this experiment stands outside the history of tragedy, telling us nothing about the evolution of the genre; it does not derive from the tragedies that immediately preceded the Suppliants, and it exerted no influence on the development of Attic tragedy

How a Woman Can Be More Like a Man: The Dialogue Between Ischomachus and his Wife in Xenophone\u27s \u3cem\u3eOeconomicus\u3c/em\u3e

The dialogue between the model Athenian landowner Ischomachus and his wife recounted in Xenophon\u27s Oeconomicus appears to offer a rare glimpse of the inner workings of an -ordinary Athenian household and a rare portrait of an ordinary Athenian wife. Through Ischoma­chus\u27s report to Socrates of a series of conversations in which he instructed his wife in her proper activities. the dialogue provides both an account of the occupations of an Athenian wife and observations on her role in the household by both herself and her husband