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.
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.104
Keywords: perfect matching association scheme, content evaluation of symmetric functions, Gelfand–Tsetlin vectors.
Srinivasan, Murali K. 1
@article{ALCO_2020__3_3_559_0, author = {Srinivasan, Murali K.}, title = {The perfect matching association scheme}, journal = {Algebraic Combinatorics}, pages = {559--591}, publisher = {MathOA foundation}, volume = {3}, number = {3}, year = {2020}, doi = {10.5802/alco.104}, zbl = {1441.05240}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.104/} }
TY - JOUR AU - Srinivasan, Murali K. TI - The perfect matching association scheme JO - Algebraic Combinatorics PY - 2020 SP - 559 EP - 591 VL - 3 IS - 3 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.104/ DO - 10.5802/alco.104 LA - en ID - ALCO_2020__3_3_559_0 ER -
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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