Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

From the first page of chapter 1 of George Andrews "Theory of Partitions" (Rather ominous place to get stuck):

enter image description here

What do these last two sentences mean? I don't get "where exactly $f_l$ of the $\lambda_j$ are equal to $i$." Can one of you rephrase this for me, because I don't understand what $i$ is.

share|improve this question
    
Is that better? If not, feel free to edit it yourself. –  user156822 Jun 13 at 0:35
    
Yes, much better, thanks. –  Nate Eldredge Jun 13 at 0:37
    
I think, $l$ is $i$, just you have a poor quality copy. –  studiosus Jun 13 at 0:49
    
@studiosus. That makes more sense. –  user156822 Jun 13 at 0:57
add comment

2 Answers 2

up vote 5 down vote accepted

It just means that the value $i$ is repeated $f_i$ times. For example the notation $(1^42^23^04^15^1)$ means the same as $(1,1,1,1,2,2,4,5)$. Since the parts have to add up to the integer $n$, the sum $$\sum_{i\ge1}f_ii=n$$ in this example is just another (IMHO unnecessarily complicated) way of writing $$1+1+1+1+2+2+4+5=17\ .$$

share|improve this answer
    
Oh. I see now. $i$ are the $\lambda_l$ that're repeated (for instance the values of i in yours are 1,2,3,4, and 5). Thanks: I knew it was something simple like that -- I was blanking when I looked at it. –  user156822 Jun 13 at 0:33
add comment

It means for example that $\lambda = (1^22^33^04^05^1)$ another notation for $\lambda = (1,1,2,2,2,5)$. That is the $f_l$ superscripts tells how many parts of a given size you have.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.