DLMF: Figure 26.9.2 ‣ §26.9 Integer Partitions: Restricted Number and Part Size ‣ Properties ‣ Chapter 26 Combinatorial Analysis

About the Project

26 Combinatorial Analysis Properties 26.9 Integer Partitions: Restricted Number and Part Size 26.9 Integer Partitions: Restricted Number and Part Size 26.10 Integer Partitions: Other Restrictions

\begin{picture}(170.0,110.0)(-25.0,0.0)\put(0.0,0.0){\circle*{2.0}}\put(20.0,0%
.0){\circle*{2.0}}\put(40.0,0.0){\circle*{2.0}}\put(60.0,0.0){\circle*{2.0}}%
\put(80.0,0.0){\circle*{2.0}}\put(100.0,0.0){\circle*{2.0}}\put(120.0,0.0){%
\circle*{2.0}}
\put(0.0,20.0){\circle*{2.0}}\put(20.0,20.0){\circle*{2.0}}\put(40.0,20.0){%
\circle*{2.0}}\put(60.0,20.0){\circle*{2.0}}\put(80.0,20.0){\circle*{2.0}}\put%
(100.0,20.0){\circle*{2.0}}\put(120.0,20.0){\circle*{2.0}}
\put(0.0,40.0){\circle*{2.0}}\put(20.0,40.0){\circle*{2.0}}\put(40.0,40.0){%
\circle*{2.0}}\put(60.0,40.0){\circle*{2.0}}\put(80.0,40.0){\circle*{2.0}}\put%
(100.0,40.0){\circle*{2.0}}\put(120.0,40.0){\circle*{2.0}}
\put(0.0,60.0){\circle*{2.0}}\put(20.0,60.0){\circle*{2.0}}\put(40.0,60.0){%
\circle*{2.0}}\put(60.0,60.0){\circle*{2.0}}\put(80.0,60.0){\circle*{2.0}}\put%
(100.0,60.0){\circle*{2.0}}\put(120.0,60.0){\circle*{2.0}}
\put(0.0,80.0){\circle*{2.0}}\put(20.0,80.0){\circle*{2.0}}\put(40.0,80.0){%
\circle*{2.0}}\put(60.0,80.0){\circle*{2.0}}\put(80.0,80.0){\circle*{2.0}}\put%
(100.0,80.0){\circle*{2.0}}\put(120.0,80.0){\circle*{2.0}}
\put(0.0,100.0){\circle*{2.0}}\put(20.0,100.0){\circle*{2.0}}\put(40.0,100.0){%
\circle*{2.0}}\put(60.0,100.0){\circle*{2.0}}\put(80.0,100.0){\circle*{2.0}}%
\put(100.0,100.0){\circle*{2.0}}\put(120.0,100.0){\circle*{2.0}}
\put(0.0,0.0){\line(1,0){4.0}}\put(8.0,0.0){\line(1,0){4.0}}\put(16.0,0.0){%
\line(1,0){4.0}}\put(24.0,0.0){\line(1,0){4.0}}\put(32.0,0.0){\line(1,0){4.0}}%
\put(40.0,0.0){\line(1,0){4.0}}\put(48.0,0.0){\line(1,0){4.0}}\put(56.0,0.0){%
\line(1,0){4.0}}\put(64.0,0.0){\line(1,0){4.0}}\put(72.0,0.0){\line(1,0){4.0}}%
\put(80.0,0.0){\line(1,0){4.0}}\put(88.0,0.0){\line(1,0){4.0}}\put(96.0,0.0){%
\line(1,0){4.0}}\put(104.0,0.0){\line(1,0){4.0}}\put(112.0,0.0){\line(1,0){4.0%
}}
\put(0.0,20.0){\line(1,0){4.0}}\put(8.0,20.0){\line(1,0){4.0}}\put(16.0,20.0){%
\line(1,0){4.0}}\put(24.0,20.0){\line(1,0){4.0}}\put(32.0,20.0){\line(1,0){4.0%
}}\put(40.0,20.0){\line(1,0){4.0}}\put(48.0,20.0){\line(1,0){4.0}}\put(56.0,20%
.0){\line(1,0){4.0}}\put(64.0,20.0){\line(1,0){4.0}}\put(72.0,20.0){\line(1,0)%
{4.0}}\put(80.0,20.0){\line(1,0){4.0}}\put(88.0,20.0){\line(1,0){4.0}}\put(96.%
0,20.0){\line(1,0){4.0}}\put(104.0,20.0){\line(1,0){4.0}}\put(112.0,20.0){%
\line(1,0){4.0}}
\put(0.0,40.0){\line(1,0){4.0}}\put(8.0,40.0){\line(1,0){4.0}}\put(16.0,40.0){%
\line(1,0){4.0}}\put(24.0,40.0){\line(1,0){4.0}}\put(32.0,40.0){\line(1,0){4.0%
}}\put(40.0,40.0){\line(1,0){4.0}}\put(48.0,40.0){\line(1,0){4.0}}\put(56.0,40%
.0){\line(1,0){4.0}}\put(64.0,40.0){\line(1,0){4.0}}\put(72.0,40.0){\line(1,0)%
{4.0}}\put(80.0,40.0){\line(1,0){4.0}}\put(88.0,40.0){\line(1,0){4.0}}\put(96.%
0,40.0){\line(1,0){4.0}}\put(104.0,40.0){\line(1,0){4.0}}\put(112.0,40.0){%
\line(1,0){4.0}}
\put(0.0,60.0){\line(1,0){4.0}}\put(8.0,60.0){\line(1,0){4.0}}\put(16.0,60.0){%
\line(1,0){4.0}}\put(24.0,60.0){\line(1,0){4.0}}\put(32.0,60.0){\line(1,0){4.0%
}}\put(40.0,60.0){\line(1,0){4.0}}\put(48.0,60.0){\line(1,0){4.0}}\put(56.0,60%
.0){\line(1,0){4.0}}\put(64.0,60.0){\line(1,0){4.0}}\put(72.0,60.0){\line(1,0)%
{4.0}}\put(80.0,60.0){\line(1,0){4.0}}\put(88.0,60.0){\line(1,0){4.0}}\put(96.%
0,60.0){\line(1,0){4.0}}\put(104.0,60.0){\line(1,0){4.0}}\put(112.0,60.0){%
\line(1,0){4.0}}
\put(0.0,80.0){\line(1,0){4.0}}\put(8.0,80.0){\line(1,0){4.0}}\put(16.0,80.0){%
\line(1,0){4.0}}\put(24.0,80.0){\line(1,0){4.0}}\put(32.0,80.0){\line(1,0){4.0%
}}\put(40.0,80.0){\line(1,0){4.0}}\put(48.0,80.0){\line(1,0){4.0}}\put(56.0,80%
.0){\line(1,0){4.0}}\put(64.0,80.0){\line(1,0){4.0}}\put(72.0,80.0){\line(1,0)%
{4.0}}\put(80.0,80.0){\line(1,0){4.0}}\put(88.0,80.0){\line(1,0){4.0}}\put(96.%
0,80.0){\line(1,0){4.0}}\put(104.0,80.0){\line(1,0){4.0}}\put(112.0,80.0){%
\line(1,0){4.0}}
\put(0.0,100.0){\line(1,0){4.0}}\put(8.0,100.0){\line(1,0){4.0}}\put(16.0,100.%
0){\line(1,0){4.0}}\put(24.0,100.0){\line(1,0){4.0}}\put(32.0,100.0){\line(1,0%
){4.0}}\put(40.0,100.0){\line(1,0){4.0}}\put(48.0,100.0){\line(1,0){4.0}}\put(%
56.0,100.0){\line(1,0){4.0}}\put(64.0,100.0){\line(1,0){4.0}}\put(72.0,100.0){%
\line(1,0){4.0}}\put(80.0,100.0){\line(1,0){4.0}}\put(88.0,100.0){\line(1,0){4%
.0}}\put(96.0,100.0){\line(1,0){4.0}}\put(104.0,100.0){\line(1,0){4.0}}\put(11%
2.0,100.0){\line(1,0){4.0}}
\put(0.0,0.0){\line(0,1){4.0}}\put(0.0,8.0){\line(0,1){4.0}}\put(0.0,16.0){%
\line(0,1){4.0}}\put(0.0,24.0){\line(0,1){4.0}}\put(0.0,32.0){\line(0,1){4.0}}%
\put(0.0,40.0){\line(0,1){4.0}}\put(0.0,48.0){\line(0,1){4.0}}\put(0.0,56.0){%
\line(0,1){4.0}}\put(0.0,64.0){\line(0,1){4.0}}\put(0.0,72.0){\line(0,1){4.0}}%
\put(0.0,80.0){\line(0,1){4.0}}\put(0.0,88.0){\line(0,1){4.0}}\put(0.0,96.0){%
\line(0,1){4.0}}
\put(20.0,0.0){\line(0,1){4.0}}\put(20.0,8.0){\line(0,1){4.0}}\put(20.0,16.0){%
\line(0,1){4.0}}\put(20.0,24.0){\line(0,1){4.0}}\put(20.0,32.0){\line(0,1){4.0%
}}\put(20.0,40.0){\line(0,1){4.0}}\put(20.0,48.0){\line(0,1){4.0}}\put(20.0,56%
.0){\line(0,1){4.0}}\put(20.0,64.0){\line(0,1){4.0}}\put(20.0,72.0){\line(0,1)%
{4.0}}\put(20.0,80.0){\line(0,1){4.0}}\put(20.0,88.0){\line(0,1){4.0}}\put(20.%
0,96.0){\line(0,1){4.0}}
\put(40.0,0.0){\line(0,1){4.0}}\put(40.0,8.0){\line(0,1){4.0}}\put(40.0,16.0){%
\line(0,1){4.0}}\put(40.0,24.0){\line(0,1){4.0}}\put(40.0,32.0){\line(0,1){4.0%
}}\put(40.0,40.0){\line(0,1){4.0}}\put(40.0,48.0){\line(0,1){4.0}}\put(40.0,56%
.0){\line(0,1){4.0}}\put(40.0,64.0){\line(0,1){4.0}}\put(40.0,72.0){\line(0,1)%
{4.0}}\put(40.0,80.0){\line(0,1){4.0}}\put(40.0,88.0){\line(0,1){4.0}}\put(40.%
0,96.0){\line(0,1){4.0}}
\put(60.0,0.0){\line(0,1){4.0}}\put(60.0,8.0){\line(0,1){4.0}}\put(60.0,16.0){%
\line(0,1){4.0}}\put(60.0,24.0){\line(0,1){4.0}}\put(60.0,32.0){\line(0,1){4.0%
}}\put(60.0,40.0){\line(0,1){4.0}}\put(60.0,48.0){\line(0,1){4.0}}\put(60.0,56%
.0){\line(0,1){4.0}}\put(60.0,64.0){\line(0,1){4.0}}\put(60.0,72.0){\line(0,1)%
{4.0}}\put(60.0,80.0){\line(0,1){4.0}}\put(60.0,88.0){\line(0,1){4.0}}\put(60.%
0,96.0){\line(0,1){4.0}}
\put(80.0,0.0){\line(0,1){4.0}}\put(80.0,8.0){\line(0,1){4.0}}\put(80.0,16.0){%
\line(0,1){4.0}}\put(80.0,24.0){\line(0,1){4.0}}\put(80.0,32.0){\line(0,1){4.0%
}}\put(80.0,40.0){\line(0,1){4.0}}\put(80.0,48.0){\line(0,1){4.0}}\put(80.0,56%
.0){\line(0,1){4.0}}\put(80.0,64.0){\line(0,1){4.0}}\put(80.0,72.0){\line(0,1)%
{4.0}}\put(80.0,80.0){\line(0,1){4.0}}\put(80.0,88.0){\line(0,1){4.0}}\put(80.%
0,96.0){\line(0,1){4.0}}
\put(100.0,0.0){\line(0,1){4.0}}\put(100.0,8.0){\line(0,1){4.0}}\put(100.0,16.%
0){\line(0,1){4.0}}\put(100.0,24.0){\line(0,1){4.0}}\put(100.0,32.0){\line(0,1%
){4.0}}\put(100.0,40.0){\line(0,1){4.0}}\put(100.0,48.0){\line(0,1){4.0}}\put(%
100.0,56.0){\line(0,1){4.0}}\put(100.0,64.0){\line(0,1){4.0}}\put(100.0,72.0){%
\line(0,1){4.0}}\put(100.0,80.0){\line(0,1){4.0}}\put(100.0,88.0){\line(0,1){4%
.0}}\put(100.0,96.0){\line(0,1){4.0}}
\put(120.0,0.0){\line(0,1){4.0}}\put(120.0,8.0){\line(0,1){4.0}}\put(120.0,16.%
0){\line(0,1){4.0}}\put(120.0,24.0){\line(0,1){4.0}}\put(120.0,32.0){\line(0,1%
){4.0}}\put(120.0,40.0){\line(0,1){4.0}}\put(120.0,48.0){\line(0,1){4.0}}\put(%
120.0,56.0){\line(0,1){4.0}}\put(120.0,64.0){\line(0,1){4.0}}\put(120.0,72.0){%
\line(0,1){4.0}}\put(120.0,80.0){\line(0,1){4.0}}\put(120.0,88.0){\line(0,1){4%
.0}}\put(120.0,96.0){\line(0,1){4.0}}
\put(-28.0,0.0){$(0,0)$}
\put(125.0,100.0){$(6,5)$}
\put(0.0,0.0){\line(0,1){20.0}}
\put(0.0,20.0){\line(1,0){40.0}}
\put(40.0,20.0){\line(0,1){20.0}}
\put(40.0,40.0){\line(1,0){20.0}}
\put(60.0,40.0){\line(0,1){20.0}}
\put(60.0,60.0){\line(1,0){40.0}}
\put(100.0,60.0){\line(0,1){40.0}}
\put(100.0,100.0){\line(1,0){20.0}}
\put(0.0,100.0){\circle*{5.0}}\put(20.0,100.0){\circle*{5.0}}\put(40.0,100.0){%
\circle*{5.0}}\put(60.0,100.0){\circle*{5.0}}\put(80.0,100.0){\circle*{5.0}}
\put(0.0,80.0){\circle*{5.0}}\put(20.0,80.0){\circle*{5.0}}\put(40.0,80.0){%
\circle*{5.0}}\put(60.0,80.0){\circle*{5.0}}\put(80.0,80.0){\circle*{5.0}}
\put(0.0,60.0){\circle*{5.0}}\put(20.0,60.0){\circle*{5.0}}\put(40.0,60.0){%
\circle*{5.0}}
\put(0.0,40.0){\circle*{5.0}}\put(20.0,40.0){\circle*{5.0}}
\end{picture} — Figure 26.9.2 (See in context.)

26.9 Integer Partitions: Restricted Number and Part Size 26.10 Integer Partitions: Other Restrictions

© 2010–2024 NIST / Disclaimer / Feedback; Version 1.2.0; Release date 2024-03-15.

NIST

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov