Multichains and Tableaux in Fibonacci Lattices
Research Report 99-02
Date: February 1999
An explicit bijection between multichains in the two Fibonacci
lattices Fib(r) and Z(r) is described.
Central to the bijection is the notion of generalized box-tableaux
for Fib(r) and Z(r) that count multichains in the respective
lattices, analogous to semi-standard generalized Young tableaux in
The generalized box-tableaux afford a simple combinatorial proof of
Stanley's algebraically derived result on the equinumeracy of multichains,
as well as providing another bijection between the elements in the intervals
[0,x] in Fib(r) and Z(r), in answer to a query of Stanley.
Fibonacci lattice. multichain. box-tableau. tableau. bijection.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics