Bijective evaluation of the connection coefficients of the double coset algebra
This paper is devoted to the evaluation of the generating series of the connection coefficients of the double cosets of the hyperoctahedral group. Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a partition $ν$, gives the spectral distribution of some random matrices that are...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2011-01-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2944/pdf |
| _version_ | 1827324032139132928 |
|---|---|
| author | Alejandro H. Morales Ekaterina A. Vassilieva |
| author_facet | Alejandro H. Morales Ekaterina A. Vassilieva |
| author_sort | Alejandro H. Morales |
| collection | DOAJ |
| description | This paper is devoted to the evaluation of the generating series of the connection coefficients of the double cosets of the hyperoctahedral group. Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a partition $ν$, gives the spectral distribution of some random matrices that are of interest in random matrix theory. We provide an explicit evaluation of this series when $ν =(n)$ in terms of monomial symmetric functions. Our development relies on an interpretation of the connection coefficients in terms of locally orientable hypermaps and a new bijective construction between partitioned locally orientable hypermaps and some permuted forests. |
| first_indexed | 2024-04-25T02:03:25Z |
| format | Article |
| id | doaj.art-db4cc29b8e9b42ffad61059afb719d26 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:25Z |
| publishDate | 2011-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-db4cc29b8e9b42ffad61059afb719d262024-03-07T14:49:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502011-01-01DMTCS Proceedings vol. AO,...Proceedings10.46298/dmtcs.29442944Bijective evaluation of the connection coefficients of the double coset algebraAlejandro H. Morales0Ekaterina A. Vassilieva1Department of Mathematics [MIT]Laboratoire d'informatique de l'École polytechnique [Palaiseau]This paper is devoted to the evaluation of the generating series of the connection coefficients of the double cosets of the hyperoctahedral group. Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a partition $ν$, gives the spectral distribution of some random matrices that are of interest in random matrix theory. We provide an explicit evaluation of this series when $ν =(n)$ in terms of monomial symmetric functions. Our development relies on an interpretation of the connection coefficients in terms of locally orientable hypermaps and a new bijective construction between partitioned locally orientable hypermaps and some permuted forests.https://dmtcs.episciences.org/2944/pdflocally orientable hypermapsforestsdouble coset algebraconnection coefficients[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Alejandro H. Morales Ekaterina A. Vassilieva Bijective evaluation of the connection coefficients of the double coset algebra Discrete Mathematics & Theoretical Computer Science locally orientable hypermaps forests double coset algebra connection coefficients [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Bijective evaluation of the connection coefficients of the double coset algebra |
| title_full | Bijective evaluation of the connection coefficients of the double coset algebra |
| title_fullStr | Bijective evaluation of the connection coefficients of the double coset algebra |
| title_full_unstemmed | Bijective evaluation of the connection coefficients of the double coset algebra |
| title_short | Bijective evaluation of the connection coefficients of the double coset algebra |
| title_sort | bijective evaluation of the connection coefficients of the double coset algebra |
| topic | locally orientable hypermaps forests double coset algebra connection coefficients [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2944/pdf |
| work_keys_str_mv | AT alejandrohmorales bijectiveevaluationoftheconnectioncoefficientsofthedoublecosetalgebra AT ekaterinaavassilieva bijectiveevaluationoftheconnectioncoefficientsofthedoublecosetalgebra |