All Questions
7 questions
16
votes
3
answers
2k
views
Integration of a function over 7-sphere
Suppose we have $x_1^2 + y_1^2 + x_2^2 + y_2^2 + x_3^2 + y_3^2 + x_4^2 + y_4^2 = 1$ and we define $z_j = x_j + iy_j$, where $j = 1,\,2,\,3,\,4$.
The problem is finding or approximating the ...
- 163
6
votes
0
answers
321
views
extensions of the Nekrasov-Okounkov formula
This post is related to the issues addressed in
A q,t-extension of Plancherel Measure thru Yang-Mills Theory ?
however the generalization/interpolation which John Mangual asks for looks different ...
- 2,137
3
votes
0
answers
342
views
Sum of products of irreducible characters of the symmetric group over a subgroup
When trying to build a dual formulation for lattice gauge theories using Weingarten integration I am getting sums of the kind
$$I^{m, n}_{\mu, \nu} (\sigma, \tau) = \sum_{\pi \in S_n} \chi_\mu (\pi \...
11
votes
1
answer
284
views
Asymptotic distribution of $\lambda_1$ under the $z$-measure for partitions
The following question about $z$-measures on Young diagrams came up in some ongoing work with Ofir Gorodetsky. I recall the background and then state our question below in the box.
For parameters $z$ ...
- 2,151
5
votes
1
answer
327
views
homomesy and asymptotic behaviour
For simplicity, consider an infinite locally-finite poset $\mathcal{P}$ with a unique bottom element $\perp$ whose finite order ideals obey a hook-length formula --- i.e. the number of
linear ...
- 2,137
6
votes
0
answers
298
views
Is there an Arctic Circle phenomenon for Amman-Beenker tilings?
I found some slides on tilings and one of them pertained to Amman-Beenker tilings. It looks like there is an Arctic Circle phenomenon similar to that for dominos or lozenges. Is there any ...
- 22.8k
8
votes
2
answers
990
views
What is the tropical Robinson-Schensted-Knuth correspondence?
And what are it's applications? A conceptual explanation would be great! Is there an expository note about this somewhere?
Some references have already appeared in the answers and comments below. To ...
- 85.6k