TAILIEUCHUNG - Báo cáo toán học: "More Statistics on Permutation Pairs"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: More Statistics on Permutation Pairs. | More Statistics on Permutation Pairs Jean-Marc Fedou Laboratoire Bordelais de Recherches en Informatique Universite Bordeaux I 33405 Talence France Don Rawlings t Mathematics Department California Polytehnic State University San Luis Obispo Ca. 93407 Submitted June 30 1994 Accepted October 21 1994 Abstract Two inversion formulas for enumerating words in the free monoid by -adjacencies are applied in counting pairs of permutations by various statistics. The generating functions obtained involve refinements of bibasic Bessel functions. We further extend the results to finite sequences of permutations. This work is partially supported by EC grant CHRX-CT93-0400 and PRC Maths-Info tFinancial support provided by LaBRI Université Bordeaux I 0 THE ELECTRONIC .JOURNAL OF COMBINATORICS 1 1994 R11 1 1 Introduction The study of statistics on permutation pairs was initiated by Carlitz Scoville and Vaughan 4 . Stanley 18 ạ-extended their work to finite sequences of permutations. In 6 we exploited the recursive technique of Carlitz et. al. to obtain some additional refinements. We also discussed numerous related distributions. Our purpose here is to further extend the study of statistics on finite permutation sequences. Our method is based on the theory of inversion presented in 7 . For clarity we primarily focus on permutation pairs. Let Sn denote the symmetric group on 1 2 . n . For a permutation ơ ơ 1 ơ 2 ơ n 2 Sn the descent and rise sets are defined as DesƠ i 1 i n 1 ơ i ơ i 1 comaj Ơ 2 n k k2Des Ơ corin Ơ 2 n k . k2Ris Ơ RisƠ i 1 i n 1 ơ i ơ i 1 . These sets are of course complementary relative to 1 2 . n 1 . The descent and rise numbers of Ơ are respectively defined to be the cardinalities of Des Ơ and Ris Ơ that is des ơ I Des ơ and ris ơ I Ris ơ . Furthermore let maj Ơ 2 k k2Des Ơ rin Ơ 2 k The statistics in the first column were originally referred to as the greater and lesser indices by Major MacMahon 16 . Many authors have since adopted the term major index for the .

• 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