Abstract
A transformation of [n] = 1,2, …, n is a function from the set to itself. Such a function, θ, is order-preserving if, for all i, j ∈ [n], i ≤ j⇒iθ ≤ jθ. The property of being order-preserving is maintained under composition, and the identity function is order-preserving, so the set of all order-preserving functions of [n] forms a monoid, which is denoted Q n . An element, θ, of Qn is idempoteni if θ ○ θ = θ, where ○ denotes composition of functions. This paper is an examination of combinatorial properties of the set of idempotents of Q n .
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Lavers, T.G. (1998). The Fibonacci Pyramid. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5020-0_28
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DOI: https://doi.org/10.1007/978-94-011-5020-0_28
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