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Extremal combinatorics of matrices, sequences and sets of permutations
Cibulka, Josef ; Valtr, Pavel (advisor) ; Füredi, Zoltán (referee) ; Jelínek, Vít (referee)
Title: Extremal combinatorics of matrices, sequences and sets of permutations Author: Josef Cibulka Department: Department of Applied Mathematics Supervisor: Doc. RNDr. Pavel Valtr, Dr., Department of Applied Mathematics Abstract: This thesis studies questions from the areas of the extremal theory of {0, 1}-matrices, sequences and sets of permutations, which found many ap- plications in combinatorial and computational geometry. The VC-dimension of a set P of n-element permutations is the largest integer k such that the set of restrictions of the permutations in P on some k-tuple of positions is the set of all k! permutation patterns. We show lower and upper bounds quasiexponential in n on the maximum size of a set of n-element permutations with VC-dimension bounded by a constant. This is used in a paper of Jan Kynčl to considerably improve the upper bound on the number of weak isomorphism classes of com- plete topological graphs on n vertices. For some, mostly permutation, matrices M, we give new bounds on the number of 1-entries an n × n M-avoiding matrix can have. For example, for every even k, we give a construction of a matrix with k2 n/2 1-entries that avoids one specific k-permutation matrix. We also give almost tight bounds on the maximum number of 1-entries in matrices avoiding a fixed layered...
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Generating graphs
Mohelníková, Lucie ; Dvořák, Zdeněk (advisor) ; Jelínek, Vít (referee)
Title: Generating graphs Author: Lucie Mohelníková Department: Department of Applied Mathematics Supervisor: Mgr. Zdeněk Dvořák, Ph.D., Computer Science Institute of Char- les University Abstract: The main topic of this thesis are the methods used to generate graphs from prescribed classes, especially graphs embeddable in surfaces. An im- portant technique in this context is to generate the graphs by vertex decontracti- ons. The identification of initial (irreducible) graphs is crucial for this technique. We give an overview of the results regarding the irreducible triangulations and quadrangulations of various surfaces, especially the surfaces of low genus (sphere, projective plane, Klein bottle). The main result of this work is the identification 21 irreducible triangulations which proves the result of Lawrencenko without using of information technology. Keywords: irreducible, triangulations, torus
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Obecná enumerace číselných rozkladů
Hančl, Jaroslav ; Klazar, Martin (advisor) ; Jelínek, Vít (referee)
Název práce: Obecná enumerace číselných rozklad· Autor: Jaroslav Hančl Katedra: Katedra aplikované matematiky Vedoucí diplomové práce: doc. RNDr. Martin Klazar, Dr., KAM MFF UK Abstrakt: Předložená diplomová práce se zabývá asymptotikami počítacích funkcí ideál· číselných rozklad·. Jejím hlavním cílem je zjistit největší možný asympto- tický r·st počítací funkce rozkladového ideálu, která je nekonečněkrát rovna nule. Autor se na základě znalosti asymptotik vybraných rozkladových ideál· snaží po- mocí kombinatorických a základních analytických metod odvodit odhady hledané asymptotiky. Výsledkem je za prvé slabší horní odhad, za druhé poměrně silný dolní odhad a za třetí, pro speciální třídu rozkladových ideál· je nalezen největší asymptotický r·st. Klíčová slova: íselné rozklady, asymptotika rozklad·, rozkladové ideály, počítací funkce, kombinatorická enumerace. 1
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Algebraické vlastnosti barevnosti grafů
Bulánek, Jan ; Jelínek, Vít (referee) ; Kráľ, Daniel (advisor)
We study algebraic tools for proving the existence of graph colorings and focus a classical method of Alon-Tarsi from this area. In particular, we prove Alon-Tarsi Theorem, provide examples of some known applications and give a new application to colorings of squares of cycles.
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Editor matematických výrazů
Holaň, David ; Lidický, Bernard (referee) ; Jelínek, Vít (advisor)
In the present work we study the concept and implementation of "MaEd for LATEX", a portable graphical user interface program for creating and editing of LATEX formulae. The program is designed to allow a beginner to create even complex formulae without any knowledge of underlying LATEX source code. The user can also import his own source code and the program doesn't make unnecessary changes to the imported source code, like removing comments and indentation. The concept describes how was the program's GUI designed. The LATEX commands available for creation of math formulae are described along with their syntax and level of support in the program. The work also analyzes structure of LATEX source code.
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Standard Glass Scales Calibration
Jelínek, Vít ; Fiala, Alois (referee) ; Jankových, Róbert (advisor)
This thesis deals with a more work-efficient and time-efficient method of calibration of standard glass scales, with practical use in the Czech Metrology Institute Regional Inspectorate in Brno. The desired streamlining of calibration were achieved in the use of a 3D coordinate measuring machine Micro-Vu Excel 4520. In the service software InSpec, six measuring programs were designed in the use of a standard glass scale brand SIP. The measurement uncertainties of this calibration were presented and calculated. This thesis draws up a draft proposal of the calibration procedure and drafts a formalized document of the calibration.
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Construction and production of the floorball stick blade using Fused Deposition Modeling
Jelínek, Vít ; Dvořáček, Jan (referee) ; Sedlák, Josef (advisor)
This work combines 3D printing technology (Rapid Prototyping) with the sports industry. Using mentioned modern technology was made functional model blade floorball stick, which originated in the engineering design 3D parametric software Autodesk Inventor. Work will explain the history of floorball and individual methods increasingly popular and more affordable 3D printing, through which could be modeled blade floorball stick. Conclusion contains techno-economic evaluation, where will be disclosed the pros and cons of the use of Rapid Prototyping technology in this sports industry.
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