Nestings of Matchings and Permutations and North Steps in PDSAWs
We present a simple bijective proof of the fact that matchings of $[2n]$ with N nestings are equinumerous to $\textit{partially directed self avoiding walks}$ confined to the symmetric wedge defined by $y= \pm x$, with $n$ east steps and $N$ north steps. A very similar construction connects permutat...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3611/pdf |
| _version_ | 1797270420078985216 |
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| author | Martin Rubey |
| author_facet | Martin Rubey |
| author_sort | Martin Rubey |
| collection | DOAJ |
| description | We present a simple bijective proof of the fact that matchings of $[2n]$ with N nestings are equinumerous to $\textit{partially directed self avoiding walks}$ confined to the symmetric wedge defined by $y= \pm x$, with $n$ east steps and $N$ north steps. A very similar construction connects permutations with $N$ nestings and $\textit{PDSAWs}$ remaining below the $x$-axis, again with $N$ north steps. Furthermore, both bijections transport several combinatorially meaningful parameters. |
| first_indexed | 2024-04-25T02:03:59Z |
| format | Article |
| id | doaj.art-6652d2af158b4aff81acb09dd1781f35 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:59Z |
| publishDate | 2008-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-6652d2af158b4aff81acb09dd1781f352024-03-07T14:38:06ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502008-01-01DMTCS Proceedings vol. AJ,...Proceedings10.46298/dmtcs.36113611Nestings of Matchings and Permutations and North Steps in PDSAWsMartin Rubey0Fakultät für Mathematik [Wien]We present a simple bijective proof of the fact that matchings of $[2n]$ with N nestings are equinumerous to $\textit{partially directed self avoiding walks}$ confined to the symmetric wedge defined by $y= \pm x$, with $n$ east steps and $N$ north steps. A very similar construction connects permutations with $N$ nestings and $\textit{PDSAWs}$ remaining below the $x$-axis, again with $N$ north steps. Furthermore, both bijections transport several combinatorially meaningful parameters.https://dmtcs.episciences.org/3611/pdfnestings and crossings of matchings and permutationspdsaws[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Martin Rubey Nestings of Matchings and Permutations and North Steps in PDSAWs Discrete Mathematics & Theoretical Computer Science nestings and crossings of matchings and permutations pdsaws [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Nestings of Matchings and Permutations and North Steps in PDSAWs |
| title_full | Nestings of Matchings and Permutations and North Steps in PDSAWs |
| title_fullStr | Nestings of Matchings and Permutations and North Steps in PDSAWs |
| title_full_unstemmed | Nestings of Matchings and Permutations and North Steps in PDSAWs |
| title_short | Nestings of Matchings and Permutations and North Steps in PDSAWs |
| title_sort | nestings of matchings and permutations and north steps in pdsaws |
| topic | nestings and crossings of matchings and permutations pdsaws [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/3611/pdf |
| work_keys_str_mv | AT martinrubey nestingsofmatchingsandpermutationsandnorthstepsinpdsaws |