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

- 232 Want to read
- 35 Currently reading

Published
**1974**
by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana
.

Written in English

- Set theory.

**Edition Notes**

Bibliography: p. 11.

Series | UIUCDCS-R-74-629 |

Classifications | |
---|---|

LC Classifications | QA76 .I4 no. 629, QA248 .I4 no. 629 |

The Physical Object | |

Pagination | ii, 11 p. |

Number of Pages | 11 |

ID Numbers | |

Open Library | OL5170349M |

LC Control Number | 74622001 |

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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.

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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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