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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.

2 votes
2 answers
350 views

$(q, t)$-binomial coefficients

The $q$-binomial coefficients ${n + k \choose n}_q$ can be written as a sum $${n + k \choose n}_q = \sum_{\lambda \subset (n^k)} q^{|\lambda|}\qquad (1)$$ where $(n^k) = (n, n, ..., n)$ is a partiti …
Y. Pei's user avatar
  • 247
6 votes

Viennot-type geometric description for dual RSK correspondence?

As far as I know, the Viennot's construction only works for RS algorithm taking permutations as input. For matrices there's a generalised version called matrix-ball construction, which can be found in …
Y. Pei's user avatar
  • 247
1 vote
1 answer
257 views

Name for series $\sum f_n x^n / (n! (n+k)!)$

Let $(f_n)_{n\ge0}$ be a real sequence. Then $\sum f_n {x^n \over n!}$ is called the exponential generating function of $(f_n)$. Let $k\ge0$ be a nonnegative integer. If we add another factorial $(n+ …
Y. Pei's user avatar
  • 247