279 research outputs found
A poset structure on quasifibonacci partitions
In this paper, we study partitions of positive integers into distinct
quasifibonacci numbers. A digraph and poset structure is constructed on the set
of such partitions. Furthermore, we discuss the symmetric and recursive
relations between these posets. Finally, we prove a strong generalization of
Robbins' result on the coefficients of a quasifibonacci power series.Comment: 16 pages, 6 figure
Move-minimizing puzzles, diamond-colored modular and distributive lattices, and poset models for Weyl group symmetric functions
The move-minimizing puzzles presented here are certain types of one-player
combinatorial games that are shown to have explicit solutions whenever they can
be encoded in a certain way as diamond-colored modular and distributive
lattices. Such lattices can also arise naturally as models for certain
algebraic objects, namely Weyl group symmetric functions and their companion
semisimple Lie algebra representations. The motivation for this paper is
therefore both diversional and algebraic: To show how some recreational
move-minimizing puzzles can be solved explicitly within an order-theoretic
context and also to realize some such puzzles as combinatorial models for
symmetric functions associated with certain fundamental representations of the
symplectic and odd orthogonal Lie algebras
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