2010/11/22 by Alejandro H. Morales, Morales, Alejandro H., Ekaterina A. Vassilieva +1 · 1 citation
Chemistry · Mathematics · #05A05 #05A19 #05E15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Random Matrices and Applications #math.CO #msc:05A05 #msc:05A19 #msc:05E15
paper · pdf · doi:10.48550/arxiv.1011.5001
12 pages, 5 figures
openalex publication_date 2010/11/22 · arxiv created 2010/11/23 · arxiv updated 2010/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 real 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 locally orientable partitioned hypermaps and some permuted forests.