KOMBINATORNE HOPFOVE ALGEBRE

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KOMBINATORNE HOPFOVE ALGEBRE

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dc.contributor.advisor Mijajlović, Žarko
dc.contributor.author Stojadinović, Tanja
dc.date.accessioned 2016-09-15T13:17:41Z
dc.date.available 2016-09-15T13:17:41Z
dc.date.issued 2013
dc.identifier.uri http://hdl.handle.net/123456789/4306
dc.description.abstract Multiplication and comultiplication, which de ne the structure of a Hopf algebra, can naturally be introduced over many classes of combinatorial objects. Among such Hopf algebras are well-known examples of Hopf algebras of posets, permutations, trees, graphs. Many classical combinatorial invariants, such as M obius function of poset, the chromatic polynomial of graphs, the generalized Dehn-Sommerville relations and other, are derived from the corresponding Hopf algebra. Theory of combinatorial Hopf algebras is developed by Aguiar, Bergerone and Sottille in the paper from 2003. The terminal objects in the category of combinatorial Hopf algebras are algebras of quasisymmetric and symmetric functions. These functions appear as generating functions in combinatorics. The subject of study in this thesis is the combinatorial Hopf algebra of hypergraphs and its subalgebras of building sets and clutters. These algebras appear in di erent combinatorial problems, such as colorings of hypergraphs, partitions of simplicial complexes and combinatorics of simple polytopes. The structural connections among these algebras and among their odd subalgebras are derived. By applying the character theory, a method for obtaining interesting numerical identities is presented. The generalized Dehn-Sommerville relations for ag f-vectors of eulerian posets are proven by Bayer and Billera. These relations are de ned in an arbitrary combinatorial Hopf algebra and they determine its odd subalgebra. In this thesis, the generalized Dehn-Sommerville relations for the combinatorial Hopf algebra of hypergraphs are solved. By analogy with Rota's Hopf algebra of posets, the eulerian subalgebra of the Hopf algebra of hypergraphs is de ned. The combinatorial characterization of eulerian hypergraphs, which depends on the nerve of the underlying clutter, is obtained. In this way we obtain a class of solutions of the generalized Dehn-Sommerviller relations for hypergraphs. These results are applied on the Hopf algebra of simplicial complexes. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2016-09-15T13:17:41Z No. of bitstreams: 1 phdTanjaStojadinovic.pdf: 13952229 bytes, checksum: dc0559e5ef8a8a1a64a4dd6e23582d9e (MD5) en
dc.description.provenance Made available in DSpace on 2016-09-15T13:17:41Z (GMT). No. of bitstreams: 1 phdTanjaStojadinovic.pdf: 13952229 bytes, checksum: dc0559e5ef8a8a1a64a4dd6e23582d9e (MD5) Previous issue date: 2013 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title KOMBINATORNE HOPFOVE ALGEBRE en_US
mf.author.birth-date 1977-05-02
mf.author.birth-place Jagodina en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpkinja en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Hopf algebra, hypergraph, building set, clutter, simplicial complex, quasisymmetric function, symmetric function, Dehn-Sommerville relations en_US
mf.subject.subarea Algebra, Combinatorics en_US
mf.contributor.committee Lipkovski, Aleksandar
mf.contributor.committee Petrović, Zoran
mf.contributor.committee Jojić, Duško
mf.university.faculty Mathematical Faculty en_US
mf.document.references 35 en_US
mf.document.pages 85 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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