The lattices of ideals of multizigzags and the enumeration of Fibonacci partitions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The lattices of ideals of multizigzags and the enumeration of Fibonacci partitions

Authors:

I. A. Pushkarev

Abstract:

Let u₁=1, u₂=2, u₃,... be the sequence of Fibonacci numbers. A Fibonacci partition of a natural number n is a partition of n into different Fibonacci numbers. In this paper it is proved that the set of Fibonacci partitions of a natural number, partially ordered with respect to refinement is the lattice of ideals of a multizigzag. On the basis of this theorem we obtain some results concerning the coefficients of the Taylor series of infinite products

$prodlimits_{i = 1}^{ + infty } {left( {1 + zq^{ui} } right) = 1 + sumlimits_{k = 1}^{ + infty } {a_k left( z right)q^k } }$

where $z = pm 1, - tfrac{1}{2} pm itfrac{{sqrt 3 }}{2}$ , ±i. Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 223, 1995, pp. 280–312. Translated by Yu. Yakubovich.

Keywords:

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