The perfect matching association scheme
Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 559-591.

We revisit the Bose–Mesner algebra of the perfect matching association scheme. Our main results are

  • An inductive algorithm, based on solving linear equations, to compute the eigenvalues of the orbital basis elements given the central characters of the symmetric groups.
  • Universal formulas, as content evaluations of symmetric functions, for the eigenvalues of fixed orbitals.
  • An inductive construction of an eigenvector (the so called first Gelfand–Tsetlin vector) in each eigenspace leading to a different inductive algorithm (not using central characters) for the eigenvalues of the orbital basis elements.
Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.104
Classification: 05E10,  05E05,  05E30
Keywords: perfect matching association scheme, content evaluation of symmetric functions, Gelfand–Tsetlin vectors.
Srinivasan, Murali K. 1

1 Department of Mathematics Indian Institute of Technology Bombay Powai, Mumbai 400076, India
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Srinivasan, Murali K. The perfect matching association scheme. Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 559-591. doi : 10.5802/alco.104. https://alco.centre-mersenne.org/articles/10.5802/alco.104/

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