دانلود کتاب Compositions, Rook Placements, and Permutations of Vectors

فهرست مطالب :

ACKNOWLEDGEMENTS ....................................................................................... iii CHAPTER 1 INTRODUCTION 1.1 Generating Functions and Partition Theory ........................... 1 1.2 Gaussian Polynomials ........................................................... 5 1.3 Ferrers Boards ................................................. 8 1.4 Permutation Statistics and Compositions ............................. 11 2 VECTOR VERSIONS OF Q-IDENTITIES 2.1 Inversions of Permutations and Partitions of Vectors . . . 14 2.2 The MACKOH Identity ............................... 36 3 COMPOSITIONS AND ROOK PLACEMENTS 3.1 Compositions of Vectors ..................................................... 48 3.2 Unitary Compositions ........................................................... 60 3.3 Simon Newcomb’s Problem .................................................. 66 4 COMPOSITIONS AND ROOK PLACEMENTS: Q-VERSIONS 4.1 q-Compositions ....................................................................... 84 4.2 q-Unitary Compositions ........................................................ 91 4.3 q-Rook Theory: Recursion Formulae .................................. 93 4.4 The (q-r) Simon Newcomb Problem and Unimodaliy. . . 110 3 CONCLUSION 3.1 Summary of Main Methods and Results ........................... 133 BIBLIOGRAPHY ................................................................................... 142 APPENDIX UST OF SYMBOLS