Geodesic
Bender-Knuth involutions for types \(\mathrm{B}\) and \(\mathrm{C}\)
Álvaro Gutiérrez1
1University of Bristol
The electronic journal of combinatorics, Tome 31 (2024) no. 2
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We show that the combinatorial definitions of King and Sundaram of the symmetric polynomials of types B and C are indeed symmetric, in the sense that they are invariant by the action of the Weyl groups. Our proof is combinatorial and inspired by Bender and Knuth's classic involutions for type A.
DOI : 10.37236/12571
Classification : 05E05, 05E10, 05E18, 20C33, 20G05
Mots-clés : orthogonal tableaux, insertion scheme, Knuth-Schensted- Robinson algorithm, type \(C\) Bender-Knuth involutions

Álvaro Gutiérrez  1

1 University of Bristol 
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     title = {Bender-Knuth involutions for types {\(\mathrm{B}\)} and {\(\mathrm{C}\)}},
     journal = {The electronic journal of combinatorics},
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     number = {2},
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Álvaro Gutiérrez. Bender-Knuth involutions for types \(\mathrm{B}\) and \(\mathrm{C}\). The electronic journal of combinatorics, Tome 31 (2024) no. 2. doi: 10.37236/12571

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