Using linear forms to determine the set of integers realizable by \((g_ 0,g_ 1,\dots ,g_ n)\)-trees
type: Item
instance of: scholarly article
title: Using linear forms to determine the set of integers realizable by \((g_ 0,g_ 1,\dots ,g_ n)\)-trees
zbMATH Open document ID: 0548.05024
DOI: 10.1016/0012-365X(83)90095-X
author: Charles A. Jones
published in: Discrete Mathematics
publication date: 1983-01-01T00:00:00Z
review text: The paper deals with the problem, how many leaves a tree can have whose internal nodes all have outvalences (number of immediate successors) out of \(g_ 0,g_ 1,...,g_ n\) and all of whose leaves are on the same level. Of particular interest is the conductor which is the least number, such that all \(N\geq k\) can occur as numbers of leaves for such trees. Since the number of leaves can be counted by \(1+(g_ 0-1)x_ 0+...+(g_ n-1)x_ n,\) where \(x_ i\) is the number of nodes of outvalence \(g_ i\), the integers in question are in intimate connection to the values the linear form \(\sum (g_ i-1)x_ i\) takes. Large intervals in the set of solutions are determined and bounds for the conductor are given.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 3873353
zbMATH Keywords: conductor
zbMATH Keywords: number of leaves
MaRDI profile type: Publication
cites work: On a Problem of Partitions
cites work: On a Problem of Partitions II
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cites work: Periodic oscillations of coefficients of power series that satisfy functional equations
cites work: On the correspondence between AVL trees and brother trees
cites work: On the linear diophantine problem of Frobenius.
description: scientific article; zbMATH DE number 3873353