All Questions
7 questions
8
votes
0
answers
331
views
A question related to Young symmetrizers
Let $T$ be an arbitrary Young tableau (i.e., filling of the diagram of an integer partition $\lambda$ of $n$ by the numbers from $1$ to $n$, each appearing once). Let $R(T)$ be the subgroup of ...
3
votes
0
answers
190
views
Orthogonal basis for decomposition of induced representation of derangements
Background
Let $V_n$ be the $\mathbb{C}$-module spanned by the set of derangements (permutations with no fixed points) inside the group ring of $S_n$. We make $V_n$ into a $\mathbb{C}S_n$-module ...
- 185
22
votes
2
answers
2k
views
3D generalizations of permutations, RSK correspondence, contingency tables, etc.
I want to gather facts and questions related to 3D generalizations
of permutations, RSK correspondence, contingency tables,
etc. One reason I am interested in this is because it is potentially
related ...
- 1,021
10
votes
1
answer
683
views
Analogues of the Knuth and Forgotten equivalences on permutations: have they been studied?
Consider a totally ordered alphabet $A$ of $n$ letters. Let $W$ be the set of all words over $A$ which have no two letters equal. Then, for example, we can define the Knuth equivalence on $W$ as the ...
- 33.8k
7
votes
0
answers
204
views
Bound on coefficients in Young tableuax
The following may be known, but I didn't find anything in the literature.
Background:
The irreducible representations of $S_n$ correspond to shapes of Young tableaux with $n$ elements. Let $\lambda$ ...
- 410
15
votes
3
answers
867
views
What bijection on permutations corresponds under RS to transpose?
The Robinson-Schensted correspondence is a bijection between elements of the symmetric group and ordered pairs of standard tableaux of the same shape.
Some simple operations on tableaux correspond to ...
- 44.7k
14
votes
3
answers
2k
views
Equivalence relations on permutations and pattern avoidance
I'm working on the interaction between equivalence relations on permutations and pattern avoidance. I've only considered Knuth equivalence and cyclic shifts until now and I'm looking for other ...
- 1,155