Mixed volumes of hypersimplices
In this extended abstract we consider mixed volumes of combinations of hypersimplices. These numbers, called mixed Eulerian numbers, were first considered by A. Postnikov and were shown to satisfy many properties related to Eulerian numbers, Catalan numbers, binomial coefficients, etc. We give a gen...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2015-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2488/pdf |
| _version_ | 1797270228243054592 |
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| author | Gaku Liu |
| author_facet | Gaku Liu |
| author_sort | Gaku Liu |
| collection | DOAJ |
| description | In this extended abstract we consider mixed volumes of combinations of hypersimplices. These numbers, called mixed Eulerian numbers, were first considered by A. Postnikov and were shown to satisfy many properties related to Eulerian numbers, Catalan numbers, binomial coefficients, etc. We give a general combinatorial interpretation for mixed Eulerian numbers and prove the above properties combinatorially. In particular, we show that each mixed Eulerian number enumerates a certain set of permutations in $S_n$. We also prove several new properties of mixed Eulerian numbers using our methods. Finally, we consider a type $B$ analogue of mixed Eulerian numbers and give an analogous combinatorial interpretation for these numbers. |
| first_indexed | 2024-04-25T02:00:56Z |
| format | Article |
| id | doaj.art-b21ac958b2bd4433bdba9338fba37117 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:56Z |
| publishDate | 2015-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-b21ac958b2bd4433bdba9338fba371172024-03-07T15:01:26ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502015-01-01DMTCS Proceedings, 27th...Proceedings10.46298/dmtcs.24882488Mixed volumes of hypersimplicesGaku Liu0Massachusetts Institute of TechnologyIn this extended abstract we consider mixed volumes of combinations of hypersimplices. These numbers, called mixed Eulerian numbers, were first considered by A. Postnikov and were shown to satisfy many properties related to Eulerian numbers, Catalan numbers, binomial coefficients, etc. We give a general combinatorial interpretation for mixed Eulerian numbers and prove the above properties combinatorially. In particular, we show that each mixed Eulerian number enumerates a certain set of permutations in $S_n$. We also prove several new properties of mixed Eulerian numbers using our methods. Finally, we consider a type $B$ analogue of mixed Eulerian numbers and give an analogous combinatorial interpretation for these numbers.https://dmtcs.episciences.org/2488/pdfhypersimplexmixed volumeeulerian numbers[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Gaku Liu Mixed volumes of hypersimplices Discrete Mathematics & Theoretical Computer Science hypersimplex mixed volume eulerian numbers [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Mixed volumes of hypersimplices |
| title_full | Mixed volumes of hypersimplices |
| title_fullStr | Mixed volumes of hypersimplices |
| title_full_unstemmed | Mixed volumes of hypersimplices |
| title_short | Mixed volumes of hypersimplices |
| title_sort | mixed volumes of hypersimplices |
| topic | hypersimplex mixed volume eulerian numbers [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2488/pdf |
| work_keys_str_mv | AT gakuliu mixedvolumesofhypersimplices |