LEADER 04402nam 22006735 450 001 9910300258803321 005 20220407171920.0 010 $a3-319-23618-0 024 7 $a10.1007/978-3-319-23618-6 035 $a(CKB)3710000000521708 035 $a(EBL)4179700 035 $a(SSID)ssj0001584999 035 $a(PQKBManifestationID)16265697 035 $a(PQKBTitleCode)TC0001584999 035 $a(PQKBWorkID)14865603 035 $a(PQKB)11717237 035 $a(DE-He213)978-3-319-23618-6 035 $a(MiAaPQ)EBC4179700 035 $a(PPN)190530359 035 $a(EXLCZ)993710000000521708 100 $a20151128d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCounting with symmetric functions /$fby Jeffrey Remmel, Anthony Mendes 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (297 p.) 225 1 $aDevelopments in Mathematics,$x1389-2177 ;$v43 300 $aDescription based upon print version of record 311 $a3-319-23617-2 320 $aIncludes bibliographical references and index. 327 $aPreface -- Permutations, Partitions, and Power Series -- Symmetric Functions -- Counting with the Elementary and Homogeneous -- Counting with a Nonstandard Basis -- Counting with RSK -- Counting Problems that Involve Symmetry -- Consecutive Patterns -- The Reciprocity Method -- Appendix: Transition Matrices -- References -- Index. 330 $aThis monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya?s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature. 410 0$aDevelopments in Mathematics,$x1389-2177 ;$v43 606 $aCombinatorial analysis 606 $aFunctions, Special 606 $aSequences (Mathematics) 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X 606 $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X 615 0$aCombinatorial analysis. 615 0$aFunctions, Special. 615 0$aSequences (Mathematics) 615 14$aCombinatorics. 615 24$aSpecial Functions. 615 24$aSequences, Series, Summability. 676 $a515.22 700 $aRemmel$b Jeffrey$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755662 702 $aMendes$b Anthony$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300258803321 996 $aCounting with Symmetric Functions$92536513 997 $aUNINA