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Sep
24 |
awarded | Autobiographer |
Apr
11 |
comment |
Summing Characters of the Symmetric Group over Derangements (Enumerative Combinatorics: Vol. II Ex. 7.63)
just something else to discuss about, do you have any idea what is the implication of setting $$p_1(y) = 0, \quad p_2(y) = p_3(y) = \ldots = 1.$$ May I know why are you dealing with this problem? Any research-related problem that you are looking at now? |
Mar
26 |
comment |
Other Variant of Schur Polynomials/Functions
made some edits |
Mar
26 |
revised |
Other Variant of Schur Polynomials/Functions
added 426 characters in body |
Mar
26 |
asked | Other Variant of Schur Polynomials/Functions |
Mar
9 |
awarded | Teacher |
Mar
8 |
revised |
Searching for equal subsets in a bipartite graph
added 188 characters in body; deleted 3 characters in body |
Mar
8 |
comment |
Searching for equal subsets in a bipartite graph
from what I mentioned above, by Hall's Theorem you can find a perfect matching for $U$. If you can find it for $U$, it means that you can find any proper subset with equality achieved. I wanted to point out that finding a perfect matching is the stronger version of your question. I apologize for the inconsistency in algorithm. $v$ if a single vertex if it is no incident to any edge in $M$. I have made appropriate edition regarding $L_i$ above. Please check. |
Mar
7 |
awarded | Editor |
Mar
7 |
revised |
Searching for equal subsets in a bipartite graph
added 878 characters in body |
Mar
7 |
answered | Searching for equal subsets in a bipartite graph |
Mar
6 |
comment |
Next smallest dimension of Specht Module after $(n)$, $(1^n)$, $(n-1,1)$ and $(2,1^{n-2})$
but that doesn't answer to this, isn't it? Correct me if I'm wrong :) |
Mar
6 |
asked | Next smallest dimension of Specht Module after $(n)$, $(1^n)$, $(n-1,1)$ and $(2,1^{n-2})$ |
Mar
6 |
awarded | Scholar |
Mar
6 |
awarded | Supporter |
Mar
6 |
comment |
Dimension of Specht Modules $S^\lambda$
Ah, thanks! I wonder there is a general properties/characterization on the dimension of $S^\lambda$ besides its formula =) |
Mar
6 |
accepted | Dimension of Specht Modules $S^\lambda$ |
Mar
6 |
comment |
Dimension of Specht Modules $S^\lambda$
So I guess maybe some experts in spectral graph theory may also be interested in this though XD |
Mar
6 |
comment |
Dimension of Specht Modules $S^\lambda$
Oops, because this question arises when I'm working on Cayley graph on $S_n$. Write $U_\lambda$ for the sum of all copies of $S^\lambda$ in $\mathbb{C} S_n$, then $\mathbb{C} S_n = \bigoplus_{\lambda \vdash n} U_\lambda$ and each $U_\lambda$ is an eigenspace of Cayley graph on $S_n$ with some generating set $X$. The corresponding eigenvalue will be $\eta_\lambda = \frac{1}{f^\lambda} \sum_{x \in S} \chi_\lambda (x)$ That is the motivation behind. |
Mar
6 |
awarded | Student |