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The correspondence which relates the Hanoi Graph to the Isomorphic Graph of the Odd Binomial Coefficients in Pascal's Triangle, where the adjacencies are determined by adjacency (either horizontal or diagonal) in Pascal's Triangle. The proof of the correspondence is given by the Lucas Correspondence Theorem.
See also Binomial Coefficient, Hanoi Graph, Pascal's Triangle
References
Poole, David G. ``The Towers and Triangles of Professor Claus (or, Pascal Knows Hanoi).'' Math. Mag. 67, 323-344, 1994.