منابع مشابه
The Kruskal Count
The Kruskal Count is a card trick invented by Martin Kruskal in which a magician “guesses” a card selected by a subject according to a certain counting procedure. With high probability the magician can correctly “guess” the card. The success of the trick is based on a mathematical principle related to coupling models for Markov chains. This paper analyzes in detail two simplified variants of th...
متن کاملOn Kruskal ’ S Theorem
In the first part of this paper, we consider 3 × 3 × 3 arrays with complex entries, and provide a complete self-contained proof of Kruskal’s theorem that the maximum rank is 5. In the second part, we provide a complete classification of the canonical forms of 3× 3× 3 arrays over F2; in particular, we obtain explicit examples of such arrays with rank 6. In 1989, Kruskal [6, page 10] stated witho...
متن کاملA Kruskal - Katona Type Theorem for the
We present an analog of the well-known Kruskal-Katona theorem for the poset of subspaces of PG (n; 2) ordered by inclusion. For given k; ` (k < `) and m the problem is to nd a family of size m in the set of`-subspaces of PG (n; 2), containing the minimal number of k-subspaces. We introduce two lexicographic type orders O 1 and O 2 on the set of`-subspaces, and prove that the rst m of them, take...
متن کاملThe Filter-Kruskal Minimum Spanning Tree Algorithm
We present Filter-Kruskal – a simple modification of Kruskal’s algorithm that avoids sorting edges that are “obviously” not in the MST. For arbitrary graphs with random edge weights, Filter-Kruskal runs in time O ( m + n log n log m n ) , i.e. in linear time for not too sparse graphs. Experiments indicate that the algorithm has very good practical performance over the entire range of edge densi...
متن کاملShifting shadows: the Kruskal–Katona Theorem
As we have seen, antichains and intersecting families are fundamental to Extremal Set Theory. The two central theorems, Sperner’s Theorem and the Erdős–Ko–Rado Theorem, have inspired decades of research since their discovery, helping establish Extremal Set Theory as a vibrant and rapidly growing area of Discrete Mathematics. One must, then, pay a greater than usual amount of respect to the Krus...
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ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2013
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v85i6.1