tailieunhanh - Báo cáo toán học: "The size of Fulton’s essential set"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: The size of Fulton’s essential set. | The size of Fulton s essential set Kimmo Eriksson1 and Svante Linusson2 Submitted January 2 1995 Accepted April 3 1995. Abstract The essential set of a permutation was defined by Fulton as the set of southeast corners of the diagram of the permutation. In this paper we determine explicit formulas for the average size of the essential set in the two cases of arbitrary permutations in Sn and 321-avoiding permutations in Sn. Vexillary permutations are discussed too. We also prove that the generalized Catalan numbers r k-1 ril-1 count r fc-matrices dotted with n dots that are n n 2 extendable to 321-avoiding permutation matrices. 1991 Mathematics Subject Classification. primary 05A15 secondary 05E99 14M15. 1 Introduction There is an extensive theory well presented by Macdonald 5 on the Schubert polynomial of a permutation w. Important in this theory is the diagram of w obtained from the permutation matrix of w by shading for every square i w i all squares to the east in row i and squares to the south in column w i . In a ground-breaking paper from 1992 Fulton 3 introduced the essential set of w as the set of southeast corners of the diagram of w which together with a rank function was used as a powerful tool in Fulton s algebraic treatment of Schubert polynomials and degeneracy loci. However we feel that the essential set as a combinatorial object is interesting per se deserving to be studied combinatorially. In another paper 2 we characterize the essential sets that can arise from arbitrary permutations as well as from certain classes of permutations. The present paper is devoted to enumerative aspects. Before treating the essential set though we immediately take a detour. It is well-known Knuth 4 that the Catalan number Cn 2J n 1 2n -1 2n-M n n n n-2 counts 321-avoiding permutations in Sn. We prove the following generalization fr k 1 n 2 r k 1 1 THE ELECTRONIC .JOURNAL OF COMBINATORICS 2 1995 R6 2 is the number of rectangular r -matrices with n dots that are .

• Báo cáo khoa học
• tài liệu báo cáo nghiện cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• các bài toán hay
• trình bày báo cáo
• báo cáo ngành văn học
• báo cáo tiếng anh
• nghiên cứu văn thơ
• giọng điệu trào phúng
• nghiên cứu khoa học
• báo cáo khoa học
• thơ lục bát
• chính sách phát triển
• gia đình việt nam
• nghiên cứu xã hội