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Tagged with young-tableaux catalan-numbers
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I want to count the multiplicity of specific peak sets occurring in a standard shifted tableau with some restrictions. Possibly using path counting?
Ok first some definitions:
Let a shifted diagram of some strict partition $\lambda$ be a Young tableau whose $i^{th}$ row is shifted $i-1$ spaces to the right, (I use french notation, and start ...
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Combinatorics and Catalan Numbers [duplicate]
I was asked to investigate this question and to present my findings and I would like some sense of help and direction, I am very lost:-(
2n people, all of different heights
How many ways are there ...
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1
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show that the number of standard tableau of shape $(n^2)$ is the Catalan number
How would one show that the number of standard tableau of shape $(n^2)$ is the Catalan number
$\mathrm{\frac{1}{n+1}}$$2n\choose{n}$
any help would be great.
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Intuition behind Hook Length Formula
Given a nonnegative integer $n$. Show that the Catalan number $C_n$ is the number of ways to arrange the integers $1, 2, \ldots, 2n$ as a standard Young tableau of rectangular shape with dimensions $2 ...
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What's the relation between standard Young tableaux and Catalan number?
From wikipedia, I know some basic facts about Catalan number and Young tableaux. Moreover, I know that Catalan number $C_n$ is the number of triangulations of a $n+2$-gon.
What's the relation ...
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321-avoiding permutations and RSK
I am reading through a book on enumeration and I came across a weird statement:
Using RSK (Robinson-Schensted-Knuth Correspondence), one can show that 321-avoiding permutations are Catalan objects.
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Young tableaux of shape lambda. [closed]
Consider the partition $\lambda=(m,n-m)$ of $n$ (thus $2m \ge n$).
The number of standard Young
tableaux of shape $\lambda$ is given by
$$f_{(m,n-m)} = \binom nm - \binom{n}{m+1}$$
a) Prove this ...
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