Alejandro H. Morales ; Ekaterina A. Vassilieva - Bijective evaluation of the connection coefficients of the double coset algebra

dmtcs:2944 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2944
Bijective evaluation of the connection coefficients of the double coset algebraArticle

Authors: Alejandro H. Morales 1; Ekaterina A. Vassilieva 2

  • 1 Department of Mathematics [MIT]
  • 2 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.


Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: 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]
Funding:
    Source : OpenAIRE Graph
  • Combinatorial methods, from enumerative topology to random discrete structures and compact data representations.; Funder: European Commission; Code: 208471

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