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Vyhledávací problémy a hledání kolizí pro hašovací funkce / Vyhledávací problémy a hledání kolizí pro hašovací funkceČarnoký, Samuel January 2011 (has links)
Title: Search problems and search for collisions in hash functions Author: Samuel Čarnoký Department: The Department of Algebra Supervisor: prof. RNDr. Jan Krajíček, DrSc. Supervisor's e-mail address: krajicek@karlin.mff.cuni.cz Abstract: Central points of this work are NP search problems and the existence of reductions amog them in the relativised world. Absolute separation would separate N from NP. In particular, we talk about the problem of finding collisions in hash functions that must exist due to the famous pigeonhole principle. We present a brief introduction into the topic, we define various NP search problems and recall reductions and separations. Reduction of weak version of PHP to a problem of finding a homogeneous subgraph is described and our own results are presented in the form of reduction of another variant of PHP to a problem related to finding paths in a graph. We talk about reducing the task of finding collisions in multiple functions into finding a collision in one function. Keywords: NP search, reductions, pigeonhole principle, oracles
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Inclusion-exclusion and pigeonhole principlesHung, Wei-cheng 25 June 2009 (has links)
In this paper, we will review two fundamental counting methods: inclusionexclusion and pigeonhole principles. The inclusion-exclusion principle considers
the elements of the sets satisfied some conditions, and avoids repeat counting by disjoint sets. We also use the inclusion-exclusion principle to solve the problems of Euler phi function and the number of onto functions in number theory, and derangement and the number of nonnegative integer solutions of equations in combinatorics. We derive the closed-form formula to those problems. For the forbidden positions problems, we use the rook polynomials to simplify the counting process. We also show the form of the inclusion-exclusion principle in probability, and use it to solve some probability problems.
The pigeonhole principle is an easy concept. We can establish some sets and use the pigeonhole principle to discuss the extreme value about the number of
elements. Choose the pigeons and pigeonholes, properly, and solve problems by the concept of the pigeonhole principle. We also introduce the Ramsey theorem which is an important application of the pigeonhole principle. This theorem provides a method to solve problems by complete graph. Finally, we give some contest problems about the inclusion-exclusion and pigeonhole principles to show how those principles are used.
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Kombinatorické principy ve školské matematice / Combinatorial principles in school mathematicsBŘEZINOVÁ, Jiřina January 2010 (has links)
The thesis includes delatiled explanation of combinatorial principles used in school mathematics. The single principles are explained in details and practicised. The tasks at the end of the chapter serve readers for testing acquired knoledge.
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Offentlig konst i SverigeEn studie av Egon Möller – Nielsens ”lekmaskiner” – Tufsen och ÄggetJuhlin Hoff, Maria January 2023 (has links)
No description available.
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