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- W2953052010 abstract "Let (A,B) and (C,D) denote Leonard pairs on V. We say these pairs are adjacent whenever each basis for V which is standard for (A,B) (resp. (C,D)) is split for (C,D) (resp. (A,B)). Our main results are as follows: Theorem 1. There exists at most 3 mutually adjacent Leonard pairs on V provided the dimension of V is at least 2. Theorem 2. Let (A,B), (C,D), and (E,F) denote three mutually adjacent Leonard pairs on V. There for each of these pairs, the eigenvalue sequence and dual eigenvalue sequence are in arithmetic progression. Theorem 3. Let (A,B) denote a Leonard pair on V whose eigenvalue sequence and dual eigenvalue sequence are in arithmetic progression. Then there exist Leonard pairs (C,D) and (E,F) on V such that (A,B), (C,D), and (E,F) are mutually adjacent." @default.
- W2953052010 created "2019-06-27" @default.
- W2953052010 creator A5008336300 @default.
- W2953052010 date "2005-08-22" @default.
- W2953052010 modified "2023-09-27" @default.
- W2953052010 title "Three Mutually Adjacent Leonard Pairs" @default.
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