Projects per year
Abstract
Consider an n× n× n cube Q consisting of n ^{3} unit cubes. A tripod of order n is obtained by taking the 3 n 2 unit cubes along three mutually adjacent edges of Q. The unit cube corresponding to the vertex of Q where the edges meet is called the center cube of the tripod. The function f(n) is defined as the largest number of integral translates of such a tripod that have disjoint interiors and whose center cubes coincide with unit cubes of Q. The value of f(n) has earlier been determined for n≤ 9. The function f(n) is here studied in the framework of the maximum clique problem, and the values f(10) = 32 and f(11) = 38 are obtained computationally. Moreover, by prescribing symmetries, constructive lower bounds on f(n) are obtained for n≤ 26. A conjecture that f(n) is always attained by a packing with a symmetry of order 3 that rotates Q around the axis through two opposite vertices is disproved.
Original language  English 

Pages (fromto)  271–284 
Number of pages  14 
Journal  Discrete and Computational Geometry 
Volume  61 
Issue number  2 
Early online date  18 Jun 2018 
DOIs  
Publication status  Published  15 Mar 2019 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Clique
 Monotonic matrix
 Packing
 Semicross
 Stein corner
 Tripod
 52C17
Fingerprint
Dive into the research topics of 'New Results on Tripod Packings'. Together they form a unique fingerprint.Datasets

Dataset for New Results on Tripod Packings
Östergård, P. (Creator) & Pöllänen, A. (Creator), Zenodo, 26 Apr 2018
Dataset
Projects
 1 Finished

Construction and Classification of Discrete Mathematic Structures
Kokkala, J., Laaksonen, A., Östergård, P., Szollosi, F., Pöllänen, A., Ganzhinov, M. & Heinlein, D.
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding