Has the Palásti Conjecture Been Proved?: A Criticism of a Paper with H. J. Weiner

Tanemura, Masaharu

doi:10.1017/s0021900200107880

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1982

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 1978 Weiner published a purported proof of the Palasti conjecture [17] but the validity of his proof has been challenged by several correspondents [7], [8], [13], [14], [15], 116] and we agree that his claim is not valid. Finegold and Donnell [6] published a note in 1979 on computer experiments on the twodimensional 'continuous' model with periodic boundaries by a 'fine mesh' and a 'coarse mesh' method and asserted verification of the Palasti conjecture.…”

Section: Introductionmentioning

confidence: 84%

Random sequential packing in Euclidean spaces of dimensions three and four and a conjecture of Palásti

Blaisdell

Solomon

1982

Journal of Applied Probability

View full text Add to dashboard Cite

A conjecture of Palásti [11] that the limiting packing density β d in a space of dimension d equals β d where ß is the limiting packing density in one dimension continues to be studied, but with inconsistent results. Some recent correspondence in this journal [7], [8], [13], [14], [15], [16], [18], [19], [20] as well as some other papers indicate a lively interest in the subject. In a prior study [3], we demonstrated that the conjectured value in two dimensions was smaller than the actual density. Here we demonstrate that this is also so in three and four dimensions and that the discrepancy increases with dimension.

show abstract