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Results tagged with young-tableaux
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user 6771
For standard Young tableaux, semistandard Young tableaux, and other related two-dimensional arrays of numbers like plane partitions. Including their combinatorial theory and their application in representation theory and algebraic geometry.
7
votes
bijection between number of partitions of 2n satisfying certain conditions with number of pa...
For $j\geqslant0$ let $c_j$ denote the $2$-core partition $(j,j-1,\dots,1)$.
Your conditions on partitions of $2n$ can be re-phrased as asking for $2$-restricted partitions of $2$-weight $n$ and $2$- …
- 1,570
16
votes
Accepted
Is there a short proof that the Kostka number $K_{\lambda \mu}$ is non-zero whenever $\lambd...
I think the following is a simple combinatorial argument which constructs the most dominant semistandard $\lambda$-tableau of content $\mu$ whenever $\lambda\trianglerighteq\mu$. (n.b. I haven't foll …
- 1,570
14
votes
Accepted
Dual of a Specht module
Yes, this works over $\mathbb Z$, and the pairing can be explicitly realised with polytabloids. See Section 4 of my paper "On the structure of Specht modules", J. London Math. Soc. 67 (2003) 85–102. ( …
- 1,570
8
votes
Accepted
What is the most general "two in one row for A & in one column for B" theorem?
I can't give you your desired "most general" theorem, but I can say a little about this. In (b), the condition "shape(A) is lexicographically larger than shape(B)" is much stronger than it needs to be …
- 1,570