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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 views

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 views

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 vote
0 answers
229 views

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 views

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 …