Tableaux and plane partitions of truncated shapes (extended abstract)
We consider a new kind of straight and shifted plane partitions/Young tableaux — ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted stai...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2011-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2950/pdf |
| _version_ | 1827324026550222848 |
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| author | Greta Panova |
| author_facet | Greta Panova |
| author_sort | Greta Panova |
| collection | DOAJ |
| description | We consider a new kind of straight and shifted plane partitions/Young tableaux — ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted staircase without the box in its upper right corner, i.e. truncated by a box, a rectangle truncated by a staircase and a rectangle truncated by a square minus a box. The proofs involve finding the generating function of the corresponding plane partitions using interpretations and formulas for sums of restricted Schur functions and their specializations. The number of standard tableaux is then found as a certain limit of this function. |
| first_indexed | 2024-04-25T02:03:19Z |
| format | Article |
| id | doaj.art-c9c9bb6cedd24479af07a2f3b27d21f5 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:19Z |
| publishDate | 2011-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-c9c9bb6cedd24479af07a2f3b27d21f52024-03-07T14:49:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502011-01-01DMTCS Proceedings vol. AO,...Proceedings10.46298/dmtcs.29502950Tableaux and plane partitions of truncated shapes (extended abstract)Greta Panova0Department of Mathematics [Cambridge]We consider a new kind of straight and shifted plane partitions/Young tableaux — ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted staircase without the box in its upper right corner, i.e. truncated by a box, a rectangle truncated by a staircase and a rectangle truncated by a square minus a box. The proofs involve finding the generating function of the corresponding plane partitions using interpretations and formulas for sums of restricted Schur functions and their specializations. The number of standard tableaux is then found as a certain limit of this function.https://dmtcs.episciences.org/2950/pdfplane partitionstableauxtruncated shapeshook formulasschur functions[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Greta Panova Tableaux and plane partitions of truncated shapes (extended abstract) Discrete Mathematics & Theoretical Computer Science plane partitions tableaux truncated shapes hook formulas schur functions [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Tableaux and plane partitions of truncated shapes (extended abstract) |
| title_full | Tableaux and plane partitions of truncated shapes (extended abstract) |
| title_fullStr | Tableaux and plane partitions of truncated shapes (extended abstract) |
| title_full_unstemmed | Tableaux and plane partitions of truncated shapes (extended abstract) |
| title_short | Tableaux and plane partitions of truncated shapes (extended abstract) |
| title_sort | tableaux and plane partitions of truncated shapes extended abstract |
| topic | plane partitions tableaux truncated shapes hook formulas schur functions [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2950/pdf |
| work_keys_str_mv | AT gretapanova tableauxandplanepartitionsoftruncatedshapesextendedabstract |