Geodesic
Bijective evaluation of the connection coefficients of the double coset algebra
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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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. 
@article{DMTCS_2011_special_260_a57,
     author = {Morales, Alejandro H. and Vassilieva, Ekaterina A.},
     title = {Bijective evaluation of the connection coefficients of the double coset algebra},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2944},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2944/}
}
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Morales, Alejandro H.; Vassilieva, Ekaterina A. Bijective evaluation of the connection coefficients of the double coset algebra. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2944. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2944/

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