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Saturday, May 9, 2020 | History

3 edition of On a problem of Katona on minimal separating systems. found in the catalog.

On a problem of Katona on minimal separating systems.

Andrew Chi-Chih Yao

On a problem of Katona on minimal separating systems.

by Andrew Chi-Chih Yao

  • 232 Want to read
  • 35 Currently reading

Published by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana .
Written in English

    Subjects:
  • Set theory.

  • Edition Notes

    Bibliography: p. 11.

    SeriesUIUCDCS-R-74-629
    Classifications
    LC ClassificationsQA76 .I4 no. 629, QA248 .I4 no. 629
    The Physical Object
    Paginationii, 11 p.
    Number of Pages11
    ID Numbers
    Open LibraryOL5170349M
    LC Control Number74622001

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On a problem of Katona on minimal separating systems by Andrew Chi-Chih Yao Download PDF EPUB FB2

In this note, we present a solution to Katona's problem. - Our main result is- the following theorem: Main ' core. Let [S = x a, x 1. Xn -1 }. If ln) is the smallest integer such that there exists a total separating system = J1, A.,), for S.

then f (1) = 0, f (') = 2, an 31 if.3l>n>'3l~1, CI) f (n)= 1-~ 1 if.Cited by: 9. The minimal cardinality of a completely separating system on an n-element set was established by Spencer [3].

Let S be a set of n elements, and k a fixed positive interger Katona [2] posed the problem of determining the smallest integer m for which there exists a completely separating system Cited by: 7.

The minimal cardinality of a completely separating system on an n-element set was established by Spencer [3]. Let S be a set of n elements, and k a fixed positive interger Katona [2] posed the problem of determining the smallest integer m for which. E Ak and x; E AI. For G = (V E), let g(G) denote the minimum number of subsets in an E-separating family.

Edmonds' problem is to determine g(G) for a graph G = (V E). Obviously Katona's problem is the special case of Edmonds' problem when G is a complete graph. lorem 2. Let-y(G) denote the chromatic number of a graph G = (V E).Cited by: 7. "On a Problem of Katona on Minimal Separation Systems", Andrew Chi-Chih Yao, Discrete Mathematics, 15 (), "An Almost Optimal Algorithm for Unbounded Searching", Jon Louis Bentley and Andrew Chi-Chih Yao, Information Processing Letters, 5 (), Cai, Mao-cheng, On a problem of Katona on minimal completely separating systems with restrictions (Note) (1) Cambini, A., An explicit form of the inverse of a particular circulant matrix (Com- munication) (2,3) Casse, L.R.A.

and D.G. Glynn, On the uniqueness of (q+ 1)4-arcs of PG(4, q). In this paper we define a completely separating system of an n-set, an extension of the concept of a separating system introduced by Renyi [1] for use in certain information theoretic problems.

In this paper we define a completely separating system of an n-set, an extension of the concept of a separating system introduced by Renyi [1] for use in certain information theoretic problems. We then consider the problem of finding the cardinality of a minimal completely separating system and show that this, considered as a function of n, is asymptotic to the cardinality of a minimal separating by: The problem of Diophantus and Davenport.

Diophantus of Alexandria, Arithmetics and the Book of Polygonal Num- On a problem of Katona on minimal completely separating systems Author: Andrej Dujella. A collection C of k-sets of [n] is a completely separating system if, for all distinct i, j∈[n], there is an S∈ C for which i∈S and j∉S.

Let R (n, k) denote the minimum size of such a by: 7. Books at Amazon. The Books homepage helps you explore Earth's Biggest Bookstore without ever leaving the comfort of your couch.

Here you'll find current best sellers in books, new releases in books, deals in books, Kindle eBooks, Audible audiobooks, and so much more. separating system. 3 Separating systems of sets with at most k elements Definition 2.

Let m(n,k) be the maximum search time of an optimal non-sequential strategy for finding an object in a search domain of n elements if only the binary tests tA with |A| ≤ k are admitted. A nonsequential strategy s = (tA1,tAm) is successful if and only if the sets.

A collection C of k-sets of [n] is a completely separating system if, for all distinct i; j 2 [n], there is an S 2 C for which i 2 S and j 62 S. Let R(n; k) denote the minimum size of such a C.

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