LEADER 03947nam 22007335 450 001 9910300255403321 005 20230711075302.0 010 $a1-4939-3091-5 024 7 $a10.1007/978-1-4939-3091-3 035 $a(CKB)3710000000521677 035 $a(SSID)ssj0001585095 035 $a(PQKBManifestationID)16265703 035 $a(PQKBTitleCode)TC0001585095 035 $a(PQKBWorkID)14864208 035 $a(PQKB)11174767 035 $a(DE-He213)978-1-4939-3091-3 035 $a(MiAaPQ)EBC6310455 035 $a(MiAaPQ)EBC5595681 035 $a(Au-PeEL)EBL5595681 035 $a(OCoLC)1076232898 035 $a(PPN)190533064 035 $a(EXLCZ)993710000000521677 100 $a20151012d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aEulerian Numbers /$fby T. Kyle Petersen 205 $a1st ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (XVIII, 456 p. 78 illus., 4 illus. in color.) 225 1 $aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4939-3090-7 320 $aIncludes bibliographical references and index. 327 $aEulerian Numbers -- Narayana Numbers -- Partially Ordered Sets -- Gamma-nonnegativity -- Weak Order, Hyperplane Arrangements, and the Tamari Lattice -- Refined Enumeration -- Simplicial Complexes -- Barycentric Subdivision -- Coxeter Groups -- W-Narayana Numbers -- Cubes, Carries, and an Amazing Matrix -- Characterizing f-vectors -- Combinatorics for Coxeter groups of Types Bn and Dn -- Affine Descents and the Steinberg Torus -- Hints and Solutions. 330 $aThis text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time. 410 0$aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 606 $aDiscrete mathematics 606 $aTopology 606 $aNumber theory 606 $aGroup theory 606 $aDiscrete Mathematics 606 $aTopology 606 $aNumber Theory 606 $aGroup Theory and Generalizations 615 0$aDiscrete mathematics. 615 0$aTopology. 615 0$aNumber theory. 615 0$aGroup theory. 615 14$aDiscrete Mathematics. 615 24$aTopology. 615 24$aNumber Theory. 615 24$aGroup Theory and Generalizations. 676 $a511.6 700 $aPetersen$b T. Kyle$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755510 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300255403321 996 $aEulerian numbers$91522461 997 $aUNINA