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Báo cáo toán học: "On Base Partitions and Cover Partitions of Skew Characters"

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: On Base Partitions and Cover Partitions of Skew Characters. | On Base Partitions and Cover Partitions of Skew Characters Christian Gutschwager Institut fur Algebra Zahlentheorie und Diskrete Mathematik Leibniz Universităt Hannover Welfengarten 1 D-30167 Hannover gutschwager at math dot uni-hannover dot de Submitted Apr 29 2008 Accepted Jul 22 2008 Published Jul 28 2008 Mathematics Subject Classification 05E05 05E10 14M15 20C30 Abstract In this paper we give an easy combinatorial description for the base partition B of a skew character A which is the intersection of all partitions a whose corresponding character a appears in A . This we use to construct the cover partition C for the ordinary outer product as well as for the Schubert product of two characters and for some skew characters here the cover partition is the union of all partitions whose corresponding character appears in the product or in the skew character. This gives us also the Durfee size for arbitrary Schubert products. Key words Base Partitions skew characters symmetric group skew Schur functions Schubert Calculus 1 Introduction In this paper we give upper and lower bounds for partitions a such that the corresponding character a can appear in a given outer product or Schubert product of two characters or in a skew character. We give in Remark 3.5 an easy combinatorial description for the base partition B of a skew character A which is the intersection of all partitions a whose corresponding character a appears in A . Using Gut1 Theorem 4.2 and the base partition we construct the cover partition C for the ordinary outer product as well as for the Schubert product of two characters and for some skew characters. Here the cover partition is the union of all partitions whose corresponding character appears in the product or in the skew character. THE ELECTRONIC JOURNAL OF COMBINATORICS 15 2008 N30 1 2 Notation and Littlewood Richardson Symmetries We mostly follow the standard notation in Sag . A partition A Al A2 . Al is a weakly decreasing sequence of non-negative