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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
1
vote
2
answers
391
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Numerical Determination of Generating Functions from Recursion Relations
Are there computer packages which calculate coefficients of generating functions, such as
$$D_n(q)=\sum_m d_{m,n}q^m= \frac{1}{\prod_{i=1}^n (1-q^i)^2} \text{ or}$$
$$S_d(q)=\sum_m s_{m,d}q^m = \fra …
4
votes
0
answers
151
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Differences of Numbers of Helicity States in 4-dimensional Strings
The question whether the states in $D=2m + 2$ dimensional string theory,
which carry a representation of $SO(2m)$, span spaces which carry
representations of $SO(2m+1)$ seems hopelessly complicated.
…
1
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0
answers
229
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Semi-Standard Young Tableaux: Do Diagrams for $O(2m)$ combine to Diagrams from $O(2m+1)$?
Let $n_\lambda^K$ be the number all semi-standard Young tableaux of size
$K$ with Ferrers diagrams diagram $\lambda$
(i.e. the number of all fillings of $\lambda$ with natural numbers with weakly i …
4
votes
1
answer
667
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Semi-Standard Young Diagrams and Families
In connection with string theory I encountered the following problem:
Given the set M_N of all semi-standard Young tableaux
of size N (i.e. all fillings of Ferrers diagrams with natural
numbers with …