DOAJ
Open Access
2009
A bijection between noncrossing and nonnesting partitions of types A and B
Ricardo Mamede
Abstrak
The total number of noncrossing partitions of type $\Psi$ is the $n$th Catalan number $\frac{1}{ n+1} \binom{2n}{n}$ when $\Psi =A_{n-1}$, and the binomial coefficient $\binom{2n}{n}$ when $\Psi =B_n$, and these numbers coincide with the correspondent number of nonnesting partitions. For type $A$, there are several bijective proofs of this equality; in particular, the intuitive map, which locally converts each crossing to a nesting, is one of them. In this paper we present a bijection between nonnesting and noncrossing partitions of types $A$ and $B$ that generalizes the type $A$ bijection that locally converts each crossing to a nesting.
Topik & Kata Kunci
Penulis (1)
R
Ricardo Mamede
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2009
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2686
- Akses
- Open Access ✓