02812nam 2200589 450 991078861700332120180731044135.00-8218-9955-4(CKB)3360000000464068(EBL)3113654(SSID)ssj0000973502(PQKBManifestationID)11582532(PQKBTitleCode)TC0000973502(PQKBWorkID)10960124(PQKB)10825147(MiAaPQ)EBC3113654(RPAM)327121(PPN)195410378(EXLCZ)99336000000046406820750530h19751975 uy| 0engur|n|---|||||txtccrFacing up to arrangements face-count formulas for partitions of space by hyperplanes /Thomas ZaslavskyProvidence :American Mathematical Society,[1975]©19751 online resource (115 p.)Memoirs of the American Mathematical Society ;volume 1, issue 1, number 154 (January 1975)"Volume 1, issue 1."Substantially the author's thesis, Massachusetts Institute of Technology.0-8218-1854-6 Includes bibliographical references.""3. Quick proofs (Eulerian method)""""AB. Proof of the whole-space cases""; ""C. The bounded case and the bounded space""; ""4. The long proofs (Tutte-Grothendieck method)""; ""A. Proof of the Euclidean case""; ""B. Proof of the projective case""; ""C. Proof of the bounded case""; ""5. A collocation of corollaries""; ""A. The Euler relations proved""; ""B. More counting relations""; ""C. Enumeration in the classical style""; ""D. Unbounded faces""; ""E. Back to Buck: arrangements made simple""; ""F. Winder's Theorem and threshold functions""; ""6 Points and zonotopes""""A. Placing hyperplanes between points""""B. The faces of zonotopes""; ""PART II. A STUDY OF EUCLIDEAN ARRANGEMENTS WITH PARTICULAR REFERENCE TO BOUNDED FACES""; ""7. The beta theorem. Theorem D""; ""8. The central decomposition. Theorem E""; ""A. Appendix on spanning sets of coatoms""; ""9. The dimension of the bounded space""; ""References""; ""Index of symbols""Memoirs of the American Mathematical Society ;number 154.Combinatorial geometryCombinatorial enumeration problemsLattice theoryCombinatorial geometry.Combinatorial enumeration problems.Lattice theory.516/.13Zaslavsky Thomas1542988MiAaPQMiAaPQMiAaPQBOOK9910788617003321Facing up to arrangements3796217UNINA