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4
votes
1answer
340 views

More asymptotics for trees

This is a follow up to my recent question on the asymptotics of A003238. Lucia gave a fine answer to that question, but as I hinted the 'real' problem I have in mind is slightly different, and I've ...
6
votes
0answers
201 views

Counting Selections of Entries such having an Extremal Permutation of length n^2+1

Let $S_{n^2+1}$ be permutations of length $n^2+1$. By Erdos-Szekeres Theorem. any $s \in S_{n^2+1}$ would have a monotone subsequence(increasing or decreasing)of length $n+1$. Say a permutation $s$ of ...
5
votes
0answers
659 views

On “The Average Height of Planted Plane Trees” by Knuth, de Bruijn and Rice (1972)

I am trying to derive the classic paper in the title only by elementary means (no generating functions, no complex analysis, no Fourier analysis) although with much less precision. In short, I "only" ...
3
votes
0answers
72 views

Counting perfect matchings with integrals

Has anyone used the Joni-Rota-Godsil integral formula (see details below) to count perfect matchings of square-grid graphs, Aztec diamond graphs, hexagon-honeycomb graphs, etc.? (Or even just to ...
3
votes
0answers
91 views

Enumerating simple algebraic groups and their irreducible representations

Motivation Everything is over an algebraically closed field. Given a faithful representation $G \to \textrm{GL}(V)$, one may try to pin down what the group $G$ exactly is (e.g., the in the case of ...
1
vote
0answers
249 views

An Pure intriguing counting problem of index sets

Hi Guys. The problem here seems like a homework, but I think that it is not that easy.It comes from a theorem I recently proved.The content of the theorem is not important, the issue is that I have no ...
0
votes
0answers
256 views

Enumerating m-tuples of Integers Subject to Implication Constraints

How do I enumerate all $m$-tuples of positive integers $(a_1,...,a_m)$ subject to the following constraints? For each $i$ in \${ 1,\ldots,m }\$, there is a number $n_i \geq 0$ such that $a_i \leq ...