Questions tagged [bijective-combinatorics]

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13
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2answers
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Automated search for bijective proofs

In enumerative combinatorics, a bijective proof that $|A_n| = |B_n|$ (where $A_n$ and $B_n$ are finite sets of combinatorial objects of size $n$) is a proof that constructs an explicit bijection ...
12
votes
0answers
213 views

Bijective proof of an identity involving number of standard Young tableaux and semistandard tableaux

Question. Can you find a bijective proof of the identity $$ \operatorname{dim}(S^{\lambda} \mathbb{C}^m)\ \operatorname{dim}(S^{\lambda'} \mathbb{C}^n) \ f^{n^m} = \dim \Lambda^p (\mathbb{C}^m \...
8
votes
1answer
395 views

Curious Catalan convolutions

Question. Do these identities involving even-index Catalan numbers have a known combinatorial interpretation? They look as though they should. I haven’t seen one in the literature. $$\sum_{a+b=n}C_{...