TAILIEUCHUNG - Báo cáo toán học: " Enumeration of standard Young tableaux of certain truncated shapes"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Enumeration of standard Young tableaux of certain truncated shapes. | Enumeration of standard Young tableaux of certain truncated shapes Ron M. Adin Ronald C. King Department of Mathematics School of Mathematics Bar-Ilan University University of Southampton Ramat-Gan 52900 Israel Southampton SO17 1BJ United Kingdom radin@ Yuval Roichman Department of Mathematics Bar-Ilan University Ramat-Gan 52900 Israel yuvalr@ Dedicated to Doron Zeilberger on the occasion of his 60th birthday. Mazal Tov Submitted Dec 16 2010 Accepted Jun 23 2011 Published Aug 26 2011 Mathematics Subject Classification Primary 05A15 Secondary 05E10. Abstract Unexpected product formulas for the number of standard Young tableaux of certain truncated shapes are found and proved. These include shifted staircase shapes minus a square in the NE corner rectangular shapes minus a square in the NE corner and some variations. 1 Introduction A truncated shape is obtained from a Ferrers diagram in the English notation where parts decrease from top to bottom by deleting cells from the NE corner. Interest in the enumeration of standard Young tableaux of truncated shapes is enhanced by a recent result 1 Prop. the number of geodesics between distinguished pairs of antipodes in Two of the authors RMA and YR were partially supported by internal research grants from Bar-Ilan University. THE ELECTRONIC JOURNAL OF COMBINATORICS 18 2 2011 P20 1 the flip graph of triangle-free triangulations is equal to twice the number of Young tableaux of a truncated shifted staircase shape. Motivated by this result extensive computations were carried out for the number of standard Young tableaux of these and other truncated shapes. It was found that in certain distinguished cases all prime factors of these numbers are relatively small hinting at the existence of product formulas. In this paper such product formulas are proved for rectangular and shifted staircase shapes truncated by a square or nearly a square. A different method to derive product .

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