DOAJ Open Access 2020

Parking functions, tree depth and factorizations of the full cycle into transpositions

John Irving Amarpreet Rattan

Lihat Sumber DOI

Abstrak

Consider the set Fn of factorizations of the full cycle (0 1 2 · · · n) ∈ S{0,1,...,n} into n transpositions. Write any such factorization (a1 b1) · · · (an bn) with all ai < bi to define its lower and upper sequences (a1, . . . , an) and (b1,...,bn), respectively. Remarkably, any factorization can be uniquely recovered from its lower (or upper) sequence. In fact, Biane (2002) showed that the simple map sending a factorization to its lower sequence is a bijection from Fn to the set Pn of parking functions of length n. Reversing this map to recover the factorization (and, hence, upper sequence) corresponding to a given lower sequence is nontrivial.

Topik & Kata Kunci

Mathematics

Penulis (2)

John Irving

Amarpreet Rattan

Format Sitasi

APA MLA BibTeX

Irving, J., Rattan, A. (2020). Parking functions, tree depth and factorizations of the full cycle into transpositions. https://doi.org/10.46298/dmtcs.6340

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6340

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6340
Akses: Open Access ✓