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3
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2answers
1k views

How to compute the rook polynomial of a Ferrers board?

Given a Ferrers board of shape $(b_1,\ldots,b_m)$, we define $r_k$ as number of ways to place $k$ non-attacking rooks (as in Chess). In section 2.4 of Stanley's Enumerative Combinatorics (vol. 1) it's ...
-1
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2answers
528 views

Where do I turn for help with generating functions?

Please forgive me if this is inappropriate for MathOverflow. I've been working/playing with generating functions for a little while and may have stumbled upon a new technique or methodology. The ...
3
votes
2answers
428 views

Euler characteristics and operator indices as exponents for Laurent polynomials

This question is rather vague. Are there any natural situations which involve Laurent polynomials of the form $$\sum q^{a_i}\in\mathbb{Z}[q,q^{-1}]$$ where the $a_i$'s are either Euler characteristics ...
9
votes
2answers
837 views

Can you find linear recurrence relation for dimensions of invariant tensors?

Let $V$ be a finite dimensional highest weight representation of a (semi)-simple Lie algebra. For each $n\ge 0$ take $a_n$ to be the dimension of the space of invariant tensors in $\otimes^n V$. In ...
2
votes
0answers
791 views

Which Hadamard Products of Generating Functions Are Known?

The Hadamard product, Schur product, or entrywise product of two generating functions is computed as follows: The Hadamard Product, H(x), given two generating functions f(x) and g(x) where $$ f(x) = ...
8
votes
2answers
729 views

What classes am I missing in the Picard lattice of a Kummer K3 surface?

Constructing the Kummer K3 of an Abelian surface $A$, we have an obvious 22-dimensional collection of classes in $H^2(K3, \mathbb{Z})$ given by the 16 (-2)-curves (which by construction do not ...
2
votes
5answers
573 views

Generating-functions: is there a relationship between a generating function and the corresponding squared generating function

Let's say we have a sequence $T(n)$ with the corresponding generating function $$A(t) = \sum_{n = 0}^\infty T(n) t^n$$ Is there some relationship between the two functions $A(t)$ and $A(t^2)$? And ...
4
votes
3answers
1k views

Asymptotics of a hypergeometric series/Taylor series coefficient.

I was planning on figuring this problem out for myself, but I also wanted to try out mathoverflow. Here goes: I wanted to know the asymptotics of the sum of the absolute values of the Fourier-Walsh ...