---
# System prepended metadata

title: discrete 7-3 赫斯圖

---

# discrete 7-3 赫斯圖


```graphviz 
digraph LR { 
// rankdir=LR;
		1 -> 2 
		2 -> 4 
	    1 -> 4 
        1 -> 3 
	} 
```
hasse diagram
## Verify partial ordering
if $R$ have reflexive, transitive, antisymetric
```graphviz 
digraph LR { 
// rankdir=LR;
		1 -> 2 
		2 -> 4  
        1 -> 3 
	} 
```

作業7
```graphviz 
digraph LR { 
// rankdir=LR;
		3 -> 2 
		3 -> 1  
        1 -> 4 
	} 
```


 least upper bound (lub)
 greatest lower bound (glb)
 
 
 $E_1$ B={{1}{2}}
 glb = $\varnothing$  
 lub = {1,2}
 $E_2$ B={{1}{1,2},{1,3},{1,2,3}}
 glb = {1}
 lub = {1,2,3}

![](https://i.imgur.com/NHd8VJF.png)
只適用在$p^{e_1}q^1$
從上排序到下，一直取upper bound，就會很像一直取+號，+號要比-號多。
從上排序到下，一直取lower bound，就會很像一直取-號，-號要比+號多。
所以所有排序方法數就是1-5的爬樓梯與括號匹配問題
n=$e_1+1$
$\frac{1}{n+1}C^{2n}_n$

(a) 24 = $2^3*3$, ans =$\frac{1}{4+1}C^{2*4}_4$=14


