LEADER 04232oam 2200637I 450 001 9910462394303321 005 20200520144314.0 010 $a0-429-10724-2 010 $a1-4398-5052-6 024 7 $a10.1201/b12210 035 $a(CKB)2670000000210865 035 $a(EBL)952022 035 $a(OCoLC)798535755 035 $a(SSID)ssj0000677061 035 $a(PQKBManifestationID)11415832 035 $a(PQKBTitleCode)TC0000677061 035 $a(PQKBWorkID)10693202 035 $a(PQKB)11679928 035 $a(MiAaPQ)EBC952022 035 $a(CaSebORM)9781439850527 035 $a(Au-PeEL)EBL952022 035 $a(CaPaEBR)ebr10574388 035 $a(CaONFJC)MIL581228 035 $a(EXLCZ)992670000000210865 100 $a20180331d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCombinatorics of permutations /$fMiklos Bona 205 $a2nd ed. 210 1$aBoca Raton, Fla :$cCRC Press,$d2012. 215 $a1 online resource (474 p.) 225 1 $aDiscrete mathematics and its applications 300 $aA Chapman and Hall book. 311 $a1-4398-5051-8 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Dedication; Contents; Foreword; Preface to the First Edition; Preface to the Second Edition; Acknowledgments; No Way around It. Introduction; 1. In One Line and Close. Permutations as Linear Orders; 2. In One Line and Anywhere. Permutations as Linear Orders. Inversions; 3. In Many Circles. Permutations as Products of Cycles; 4. In Any Way but This. Pattern Avoidance. The Basics; 5. In This Way, but Nicely. Pattern Avoidance. Follow-Up; 6. Mean and Insensitive. Random Permutations; 7. Permutations and the Rest. Algebraic Combinatorics of Permutations 327 $a8. Get Them All. Algorithms and Permutations9. How Did We Get Here? Permutations as Genome Rearrangements; Do Not Look Just Yet. Solutions to Odd-Numbered Exercises; References; List of Frequently Used Notation 330 $aPreface to the Second Edition It has been eight years since the first edition of Combinatorics of Permutations was published. All parts of the subject went through significant progress during those years. Therefore, we had to make some painful choices as to what to include in the new edition of this book. First, there is a new chapter to this edition, Chapter 9, which is devoted to sorting algorithms whose original motivation comes from molecular biology. This very young part of combinatorics is known for its easily stated and extremely difficult problems which sometimes can be solved using deep techniques from remote-looking parts of mathematics. We decided to discuss three sorting algorithms in detail. Second, half of the existing chapters, namely Chapters 1, 3, 4, and 6 have been significantly changed or extended. Chapter 1 has a new section on Alternating Permutations, while Chapter 3 has new material on multivariate applications of the Exponential Formula. In Chapter 4, which discusses pattern avoidance, several important results, some in the text, some in the exercises, have been improved. Chapter 6, discussing some probabilistic aspects of permutations, now covers the concept of asymptotically normal distributions. Third, all chapters have an extended Exercises section and an extended Problems Plus section. The latter often contains results from the last eight years. Exercises marked with a (+) sign are thought to be more difficult than average, while exercises marked with a (-) sign are thought to be easier. The book does not assume previous knowledge of combinatorics above the level of an introductory undergraduate course--$cProvided by publisher. 410 0$aDiscrete mathematics and its applications. 606 $aPermutations 606 $aCombinatorial analysis 608 $aElectronic books. 615 0$aPermutations. 615 0$aCombinatorial analysis. 676 $a511/.64 700 $aBona$b Miklos.$0420999 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462394303321 996 $aCombinatorics of permutations$91020423 997 $aUNINA