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Steinhaus triangles
dc.contributor | Maureso Sánchez, Montserrat |
dc.contributor | Brunat Blay, Josep Maria |
dc.contributor.author | Pascual Miranda, Núria |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-01-26T10:36:55Z |
dc.date.available | 2016-01-26T10:36:55Z |
dc.date.issued | 2016-01 |
dc.identifier.uri | http://hdl.handle.net/2117/82029 |
dc.description.abstract | In this thesis, we study Steinhaus's problem. We begin with the definitions of Steinhaus triangle and balanced binary sequence, and we study sequences with different properties. We then show three different proofs of the existence of balanced binary sequences of any length n ≡ 0 or 3 (mod 4). In the last chapter, we present Molluzzo s problem, a generalization of Steinhaus s problem. We study arithmetic progressions and antisymmetric sequences and their associated generalized triangles. On the one hand, we show the existence of balanced sequences in Z/3 k Z of any valid length. On the other hand, we see different cases in which Molluzzo s problem is answered negatively. |
dc.language.iso | eng |
dc.publisher | Universitat Politècnica de Catalunya |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
dc.subject.lcsh | Combinatorial analysis |
dc.subject.other | Steinhaus's problem |
dc.subject.other | Steinhaus triangle |
dc.subject.other | Binary sequence |
dc.subject.other | Balanced |
dc.subject.other | Strongly-balanced |
dc.subject.other | Zero-sum |
dc.subject.other | Molluzzo's problem |
dc.title | Steinhaus triangles |
dc.type | Bachelor thesis |
dc.subject.lemac | Combinacions (Matemàtica) |
dc.subject.ams | Classificació AMS::05 Combinatorics |
dc.identifier.slug | FME-1280 |
dc.rights.access | Open Access |
dc.date.updated | 2016-01-23T06:39:05Z |
dc.audience.educationlevel | Grau |
dc.audience.mediator | Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística |
dc.audience.degree | GRAU EN MATEMÀTIQUES (Pla 2009) |