整數(shù)劃分的計(jì)算方法及其在不定方程中的應(yīng)用

許平,張美慧,孟健

(1.云南財(cái)經(jīng)大學(xué)統(tǒng)計(jì)與數(shù)學(xué)學(xué)院,昆明650221;2.東北財(cái)經(jīng)大學(xué)統(tǒng)計(jì)學(xué)院,大連116025)

整數(shù)劃分的計(jì)算方法及其在不定方程中的應(yīng)用

許平1,張美慧2,孟健1

(1.云南財(cái)經(jīng)大學(xué)統(tǒng)計(jì)與數(shù)學(xué)學(xué)院,昆明650221;2.東北財(cái)經(jīng)大學(xué)統(tǒng)計(jì)學(xué)院,大連116025)

整數(shù)劃分是數(shù)論的重要問(wèn)題之一. 該研究介紹了整數(shù)劃分一種的計(jì)算方法， 并應(yīng)用于一次不定方程. 結(jié)合MATLAB程序， 計(jì)算任何一次不定方程的所有非負(fù)整數(shù)解或者正整數(shù)解及其個(gè)數(shù).

整數(shù)劃分;一次不定方程;非負(fù)整數(shù)解;正整數(shù)解

[1]陳廣.基于分豆策略的整數(shù)劃分問(wèn)題的設(shè)計(jì)與實(shí)現(xiàn)[J].福建電腦,2012(9).

[2]那履弘,婁惠元.整數(shù)劃分中的通項(xiàng)約束問(wèn)題[J].沈陽(yáng)黃金學(xué)院學(xué)報(bào),1992(3).

[3]那履弘,婁惠元.整數(shù)劃分中部分頂間的約束問(wèn)題[J].沈陽(yáng)黃金學(xué)院學(xué)報(bào),1993(1).

[4]康慶德.組合學(xué)筆記[M].北京：科學(xué)出版社,2009.

［責(zé)任編輯魯海菊］

Calculation Method for Integer Partition and its Applications in Indefinite Equations

XU Ping1,ZHANG Mei-hui2，MENG Jian1
(1.School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming 650221,China；2.School of Statistics,Dongbei University of Finance and Economics,Dalian 116025,China)

Integer partition is one of important issue of Number Theory.This study introduces a calculation method for integer partition and its application on first-order indefinite equation.The all non-negative or positive solutions and the number of those solutions of the arbitrary first-order indefinite equation could be calculated by combining with the MATLAB program.

integer partition；first-order indefinite equation；non-negative integer solution；positive integer solution

O157

A

1008-9128(2015)05-0017-06

2014-11-08

國(guó)家自然科學(xué)基金項(xiàng)目：帶有隨機(jī)效應(yīng)的廣義空間自回歸模型的統(tǒng)計(jì)推斷(11301463)

許平(1990-),男,安徽安慶人,碩士生,研究方向：數(shù)理統(tǒng)計(jì)。