Titlebook: A Journey Through Discrete Mathematics; A Tribute to Jiří Ma Martin Loebl,Jaroslav Nešetřil,Robin Thomas Book 2017 Springer International p

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Elisabeth Reitinger,Bärbel Traunsteiner Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper.

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Elisabeth Reitinger,Bärbel Traunsteinerents, where the number of variables substantially exceeds the number of equations (for example, . equations and . variables with . ≥ 2.), and “small” means small in the maximum norm. Siegel’s Lemma is a clever application of the Pigeonhole Principle, and it is a pure existence argument. The basicall

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https://doi.org/10.1007/978-3-642-85555-9s we present some of them, related to the game of HEX and to the piercing of multiple intervals. We also sketch stronger theorems, due to Oliver and others, and explain their applications to the fascinating (and still not fully solved) evasiveness problem.

FORGO

Schlussbetrachtung und Ausblick, disjoint faces in . to the same point in .. The proof of this result for the case when . is a prime, as well as some colored version of the same result, using the results of Borsuk–Ulam and Dold on the non-existence of equivariant maps between spaces with a free group action, were main topics of Ma

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Angela Nikelski,Annette Nauerthices such that every two-coloring of the edges of . contains an induced monochromatic copy of .. We study this function, showing that ..(.) is bounded above by a reasonable power of .(.). In particular, our result implies that . for any 3-uniform hypergraph . with . vertices, mirroring the best know

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https://doi.org/10.1007/978-3-658-18013-3twork, however, is of a special nature: every time the train traverses a switch, the switch will change its position immediately afterwards. Hence, the next time the train traverses the same switch, the other direction will be taken, so that directions alternate with each traversal of the switch..Gi