# Mark Wildon

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 Name Mark Wildon Member for 2 years Seen 7 hours ago Website Location Royal Holloway, University of London Age 35
 Apr10 answered Partitions-Sum of divisors identity Apr3 comment Identity involving Fresnel integralsThat's interesting. I stopped at the final integral because it can be done in a routine way with a reduction formula: write $(1-u^2)^{2n} = (1-u^2)^{2n-1} - 2u(1-u^2) u/2$ and use integration by parts on the second term. I don't know of a combinatorial proof. Apr3 accepted Identity involving Fresnel integrals Apr2 revised Identity involving Fresnel integralsedited tags Apr2 answered Identity involving Fresnel integrals Apr1 answered Motivation and Intuition for Sprague-Grundy Theorem Apr1 comment Motivation and Intuition for Sprague-Grundy TheoremJust to expand on the final line: in the game $G + \star n$, if the first player plays to $\star m$ in $G$ where $m < n$, then the second player can play in $\star n$ to give $\star m + \star m = 0$; if the first player plays to $\star m'$ in $\star n$ where $m' < n$ then the second player can play in $G$ to $\star m'$ to give $\star m' + \star m' = 0$. (We know that $\star m'$ is an option of $G$ because $n$ is the minimum excluded option.) Hence $G + \star n = 0$ and $G = \star n$. Feb21 revised Box removing operators on partitionsMany corrections. Feb20 revised Box removing operators on partitionsCorrected LaTeX. Feb20 revised Box removing operators on partitionsRepaired argument so it works for the question as posed. Feb20 revised Box removing operators on partitionsdeleted 2505 characters in body Feb20 revised Box removing operators on partitionsadded 25 characters in body Feb20 answered Box removing operators on partitions Feb16 accepted Known decomposition of $\bigwedge^k Sym^d \mathbb C^n$ in special cases? Feb15 comment Known decomposition of $\bigwedge^k Sym^d \mathbb C^n$ in special cases?Thank you for the reference. As you say in your paper, it's a remarkable isomorphism. Feb14 revised Known decomposition of $\bigwedge^k Sym^d \mathbb C^n$ in special cases?Forgot to say that \lambda has distinct parts Feb14 comment Known decomposition of $\bigwedge^k Sym^d \mathbb C^n$ in special cases?When $n=2$ the plethysm ${\rm Sym^k}{\rm Sym^d}V$ is given by the Cayley-Sylvester formula. I can't see why this is equivalent to knowing your plethysm. But I think it should be possible to work out the constituents of $\bigwedge^k ({\rm Sym}^d V)$ using similar arguments with formal characters of ${\rm SL_2}(\mathbb{C})$. Feb14 answered Known decomposition of $\bigwedge^k Sym^d \mathbb C^n$ in special cases? Jan12 comment An inequality for the ratio of standard Young tableau with {1,2,…,k} in the first rowI agree with darij grinberg's comment. Do you know if there is a refinement to a chain of results: $\frac{\dim \lambda / (k)}{\dim \beta / (k)} \ge \frac{\dim \lambda / (k-1)}{\dim \beta / (k-1)}$ for $k \ge 1$?