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Tagged with young-tableaux generating-functions
3
questions
0
votes
0
answers
123
views
How to evaluate $s_\lambda(q,q^2,\cdots,q^m)$? (principal specialisation of the schur function)
It is required to show that
$$
s_\lambda(q,q^2,\cdots,q^m) = q^{m(\lambda)}\prod_{i,j \in \lambda}\frac{1-q^{c_{i,j}+m}}{1-q^{h_{i,j}}}
$$
where $c_{i,j}=j-i$ is the content of cell $(i,j)$, and $h_{i,...
user614535
2
votes
1
answer
428
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Generating function of Young Diagram from a given semiperimeter
so my question is:
What is the generating function for the number of Young diagrams of a given semiperimeter?
My approach: knowing that there exists a diagram with zero boxes, $$a_0=1$$$$a_1=2$$ $$....
- 43
0
votes
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Combinatorial identity
Let $a_1,\cdots,a_n$ be n positive consecutive integers. So I want to know if there exists a close combinatorial form for the coefficient of $x^k$ in
$$(x+a_1)(x+a_2)\ldots (x+a_n) .$$
In ...
- 1,065