On Replace Function and Swap Function for Finite Sequences

Hiroshi Yamazaki

Shinshu University, Nagano

Yoshinori Fujisawa

Shinshu University, Nagano

Yatsuka Nakamura

Shinshu University, Nagano

Summary.

In this article, we show the property of the Replace Function and the Swap Function of finite sequences. In the first section, we prepared some useful theorems for finite sequences. In the second section, we defined the Replace function and proved some theorems about the function. This function replaces an element of a sequence by another value. In the third section, we defined the Swap function and proved some theorems about the function. This function swaps two elements of a sequence. In the last section, we show the property of composed functions of the Replace Function and the Swap Function.

MML Identifier: FINSEQ_7

Contents (PDF format)

1. Some Basic Theorems
2. Definition of Replace Function and its Properties
3. Definition of Swap Function and its Properties
4. Properties of Combination Function of Replace Function and Swap Function

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