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A potential difference combined cycle generation method of a Kokmann ternary system

A technology of difference combination and generation method, which is applied in the field of cyclic generation method of disparity combination of Kirkman ternary system. It can solve the problem of no theoretical demonstration, no proof whether the solution is isomorphic, and no Kirkman ternary system construction problem. Unification and other issues to achieve the effect of concise and easy to understand

Pending Publication Date: 2019-06-28
FUJIAN JIANGXIA UNIV
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Problems solved by technology

[0003] Since Kirkman proposed the girl's walking problem in 1850, many scholars and enthusiasts have conducted many studies and discussions on the construction of Kirkman's ternary system, but these problems are common. First, it has not been proved whether the given solution is Isomorphism; the second has no theoretical argument, only the specific arrangement is given; the third method is only for the Kirkman ternary system with an order of 15, and does not propose a unity for the construction of the Kirkman ternary system Methods

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  • A potential difference combined cycle generation method of a Kokmann ternary system
  • A potential difference combined cycle generation method of a Kokmann ternary system
  • A potential difference combined cycle generation method of a Kokmann ternary system

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Embodiment Construction

[0028] The technical solution of the present invention will be specifically described below in conjunction with the accompanying drawings.

[0029] The present invention provides a method for generating the potential difference combination cycle of the Kirkman ternary system, which is realized as follows:

[0030] Suppose a combination design is composed of two finite sets X, β and the relation I between them, denoted as D=(X, β, I), X set is a point set, β set is an interval set;

[0031] Correspond the points on the X set {1,2,3,...,v} to the equally divided circle and the center of the circle, that is, divide the circle into (v-1) equally, and divide 1,2,3,... , v-1 is marked on the equal point of the circle, and v is marked on the center of the circle; any two points on the circle are connected, that is, the length of the chord length is represented by the potential difference Dis(i,j), for j∈{1 ,2,3,...,v-1}, i∈{1,2,3,...,v-1} have:

[0032]

[0033] Because the poin...

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Abstract

The invention relates to a potential difference combined cycle generation method of a Kokmann ternary system. According to the method, points on an X set correspond to equant circumferences and circlecenters, concepts of potential difference and combined potential difference are provided, characteristics of two kinds of triangles on a circle are studied, a unified method for solving the problem of the Kokmann ternary system is further provided, and the generated Kokmann ternary system is not isomorphic. According to the method, KTS (v) is generated without complex mathematical tools such as algebraic theory, the method is visual, vivid, simple, clear and easy to understand, and the method is irrelevant to the order v.

Description

technical field [0001] The invention provides a method for solving the construction problem of the Kirkman ternary system, and specifically relates to a method for corresponding points on the equally divided circle and the center of the circle, and on the basis of the concepts of potential difference and potential difference combination, it is proposed to generate a Kirkman ternary The condition of the sequence of potential difference combinations of the system is given, and the generation method of the potential difference combination cycle for the construction problem of the Kirkman ternary system is given. Background technique [0002] The girl's walk problem proposed by Kirkman in 1850, and the existence and large set problems of the general Kirkman ternary system in combinatorics derived from the "Kirkman girl's walk problem" began to be studied. In 1971, it was proved by Ray Chaud Hurley and Wilson that v≡3(mod6) is a necessary and sufficient condition for the existenc...

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Application Information

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IPC IPC(8): G06F17/10
Inventor 谢玉枚卓琳张洁玲
Owner FUJIAN JIANGXIA UNIV