All Questions
6
questions
0
votes
2
answers
77
views
Partitioning evens as sum of evens
Take the set $\{a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8\}$.
We can partition according to rules.
Every member in the partition has even number of elements.
Every member in partition have to be consecutive.
...
- 123
2
votes
1
answer
87
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A question on an identity involving partition
Let $n$ be a natural number. Let $\lambda \mapsto n$ , be a partition of n. So $\lambda=(\lambda_1, \lambda_2, \ldots ,\lambda_k)$, with $\lambda_1\leq \ldots \leq \lambda_k$, and $\sum_{i=1}^k \...
- 4,135
1
vote
0
answers
71
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Why is the ladder tableau of an $e$-restricted partition $e$-restricted?
Lemma 3.40 on page 46 in Mathas's "Iwahori-Hecke Algebras and the Symmetric Group" states
Suppose that $\lambda$ is an $e$-restricted partition of $n$. Then the ladder tableau $\mathfrak{l}_e^\...
- 997
1
vote
1
answer
125
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How many solutions of equation
How many solutions of equation
$x_1+x_2+x_3+x_4=n$ in $N_0$ such that $x_1\leq x_2\leq x_3 \leq x_4$?
I found solutions of $x_1+x_2+x_3=n$ in $N_0$ , $x_1\leq x_2\leq x_3 $ in the following way :
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- 153
5
votes
0
answers
284
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On Applications of the Murnaghan-Nakayama rule
The question is located below. In short, I am looking for an accessible explanation of the Murnaghan-Nakayama rule in relation to the following problem. Pardon the long setup.
Let $Y$ be a standard ...
- 32.9k
15
votes
2
answers
373
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A question on partitions of n
Let $P$ be the set of partitions of $n$. Let $\lambda$ denote the shape of a particular partition. Let $f_\lambda(i)$ be the frequency of $i$ in $\lambda$ and let $a_\lambda(i) := \# \lbrace j : f_\...
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