All Questions
4 questions
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 ...
12
votes
0
answers
643
views
Wilf's conjecture: complementary Bell numbers
The complementary Bell numbers or Uppuluri–Carpenter numbers, denoted $\tilde{B}_n$, can be delivered by
$$G(x):=\sum_{n\geq0}\tilde{B}_n\frac{x^n}{n!}=e^{1-e^x}.$$
Definition. Fix an integer $m\geq0$....
4
votes
1
answer
597
views
genus zero permutation and noncrossing partition
Question
Let $g$ to be an element of permutation group $S_n$, and $\tau = (1,2,3,\cdots,n)$ is the circular permutation. $g$ and $\tau g$ have $n+1$ cycles in total(fixed point is also a cycle), ...
4
votes
0
answers
206
views
Non-crossing and crossing bijection in higher genus
This is a follow-up question of my SO post I'll briefly mention it here.
So given a $n$ cycle say $(1,2,\ldots,n)$, what are the monotonic 2 -tuples, of the form $(a,b)(c,d)$, monotonicity in on the ...