LEADER 00834nam0 2200253 450 001 000021294 005 20090109130422.0 100 $a20090109d1971----km-y0itay50------ba 101 0 $ager$cita 102 $aIT 105 $ay-------001yy 200 1 $aVocabolario tedesco-italiano, italiano-tedesco$fA. Deidda 205 $aNuovissima ed. 210 $aOzzano Emilia [Bologna]$cMalipiero$d1971 215 $aXVI, 2454 p.$d21 cm 500 10$aVocabolario tedesco-italiano, italiano-tedesco$948089 676 $a433.51$v19$9Astronautica 700 1$aDeidda,$bArmando$4070$0443887 801 0$aIT$bUNIPARTHENOPE$c20090109$gRICA$2UNIMARC 912 $a000021294 951 $aG 433.51/1$bG 229$cDSA$d2008 951 $aG 433.51/2$bG 269$cDSA$d2008 996 $aVocabolario tedesco-italiano, italiano-tedesco$948089 997 $aUNIPARTHENOPE LEADER 04533nam 22005533 450 001 9910970102003321 005 20231110220624.0 010 $a9781470471705 010 $a1470471701 035 $a(MiAaPQ)EBC29379001 035 $a(Au-PeEL)EBL29379001 035 $a(CKB)24267882600041 035 $a(OCoLC)1336954399 035 $a(EXLCZ)9924267882600041 100 $a20220721d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDecorated Dyck Paths, Polyominoes, and the Delta Conjecture 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$d©2022. 215 $a1 online resource (138 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.278 311 08$aPrint version: D'Adderio, Michele Decorated Dyck Paths, Polyominoes, and the Delta Conjecture Providence : American Mathematical Society,c2022 9781470471576 327 $aCover -- Title page -- Introduction -- Acknowledgments -- Part 1. Definitions and results -- Chapter 1. Background and definitions -- 1.1. Symmetric and quasisymmetric functions -- 1.2. Combinatorial definitions -- Chapter 2. Conjectures -- 2.1. The Delta conjecture -- 2.2. The generalised Delta conjecture -- 2.3. Our conjecture with \pmaj -- 2.4. Our conjecture with polyominoes -- 2.5. Our square conjecture -- Chapter 3. Our results -- 3.1. A decorated , -Schröder -- 3.2. A decorated , -Narayana -- 3.3. Links with the Delta conjecture -- 3.4. A symmetry result -- 3.5. A new , -square -- 3.6. Symmetric functions identities -- 3.7. A few open problems -- Part 2. Proofs -- Chapter 4. Symmetric functions -- 4.1. Basic identities -- 4.2. A summation formula -- 4.3. Three families of plethystic formulae -- 4.4. Another symmetric function identity -- 4.5. Two theorems and a corollary -- 4.6. ?_{ } ( _{ }) at =1/ -- Chapter 5. Combinatorics of decorated Dyck paths -- 5.1. Haglund's (sweep) map -- 5.2. The map exchanging peaks and falls -- 5.3. Combinatorial recursions -- Chapter 6. Combinatorics of polyominoes -- 6.1. Parallelogram polyominoes -- 6.2. Reduced polyominoes -- 6.3. Two car parking functions -- 6.4. Partially labelled Dyck paths -- 6.5. A new \dinv statistic on parallelogram polyominoes -- 6.6. A \bounce statistic on partially labelled Dyck paths -- Chapter 7. Putting the pieces together -- 7.1. Combinatorial interpretations of plethystic formulae -- 7.2. Proof of the decorated , -Schröder -- 7.3. Proof of the decorated , -Narayana -- Chapter 8. Square paths -- 8.1. A new , -square -- 8.2. Observations when =1/ -- Appendix A. Proof of the elementary lemmas -- Bibliography -- Back Cover. 330 $a"We discuss the combinatorics of decorated Dyck paths and decorated parallelogram polyominoes, extending to the decorated case the main results of both Haglund ("A proof of the Schroder conjecture", 2004) and Aval et al. ("Statistics on parallelogram polyominoes and a analogue of the Narayana numbers", 2014). This settles in particular the cases and of the Delta conjecture of Haglund, Remmel and Wilson ("The delta conjecture", 2018). Along the way, we introduce some new statistics, formulate some new conjectures, prove some new identities of symmetric functions, and answer a few open problems in the literature (e.g., from Aval, Bergeron and Garsia [2015], Haglund, Remmel and Wilson [2018], and Zabrocki [2019]). The main technical tool is a new identity in the theory of Macdonald polynomials that extends a theorem of Haglund in "A proof of the Schroder conjecture" (2004)"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aCombinatorial analysis 606 $aSymmetric functions 606 $aCombinatorics -- Algebraic combinatorics -- Symmetric functions and generalizations$2msc 615 0$aCombinatorial analysis. 615 0$aSymmetric functions. 615 7$aCombinatorics -- Algebraic combinatorics -- Symmetric functions and generalizations. 676 $a511/.6 676 $a511.6 686 $a05E05$2msc 700 $aD'Adderio$b Michele$01734842 701 $aIraci$b Alessandro$01802306 701 $aWyngaerd$b Anna Vanden$01802307 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910970102003321 996 $aDecorated Dyck Paths, Polyominoes, and the Delta Conjecture$94347953 997 $aUNINA