DOAJ Open Access 2009

$k$-distant crossings and nestings of matchings and partitions

Dan Drake Jang Soo Kim

Lihat Sumber DOI

Abstrak

We define and consider $k$-distant crossings and nestings for matchings and set partitions, which are a variation of crossings and nestings in which the distance between vertices is important. By modifying an involution of Kasraoui and Zeng (Electronic J. Combinatorics 2006, research paper 33), we show that the joint distribution of $k$-distant crossings and nestings is symmetric. We also study the numbers of $k$-distant noncrossing matchings and partitions for small $k$, which are counted by well-known sequences, as well as the orthogonal polynomials related to $k$-distant noncrossing matchings and partitions. We extend Chen et al.'s $r$-crossings and enhanced $r$-crossings.

Topik & Kata Kunci

Mathematics

Penulis (2)

Dan Drake

Jang Soo Kim

Format Sitasi

APA MLA BibTeX

Drake, D., Kim, J.S. (2009). $k$-distant crossings and nestings of matchings and partitions. https://doi.org/10.46298/dmtcs.2746

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2746

Informasi Jurnal

Tahun Terbit: 2009
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2746
Akses: Open Access ✓