Multichains and Tableaux in Fibonacci Lattices


Rowan Kemp


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 Young's lattice.

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.

Key phrases

Fibonacci lattice. multichain. box-tableau. tableau. bijection.

AMS Subject Classification (1991)

Primary: 06B05
Secondary: 05A15


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