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Results tagged with co.combinatorics
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user 4366
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
4
votes
Accepted
The formula for a perhaps basic identity (move from stackexchange)
I guess the first product is expanded as
$$
\prod_{k=1}^n(1+x+y_k)=(1+x)^n\prod_k(1+y_k(1+x)^{-1})=\sum_{k\geq 0}e_k(y_1,\ldots,y_n)(1+x)^{-k+n}.$$
For the other products you can write
$$
\prod_{j=1}^ …
- 1,472
2
votes
1
answer
227
views
A question on Lusztig's `graph with automorphism' construction?
Using the notion of a graph with compatible automorphism, Lusztig constructs all symmetrizable Cartan data (i.e. Cartan matrices $A$ for which there is a diagonal matrix $D=\mathrm{diag}(d_1,\ldots,d_ …
- 1,472
3
votes
Are there positive formulae for the inner product between elements of a Lie algebra represen...
Ben, my paper on the Shapovalov form does give a generating series for the entries of a Gram matrix in Corollary 3.4, and those entries are evidently positive. It is not very hard to deduce a q-versi …
- 1,472