Projekteja vuodessa
Abstrakti
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.
Alkuperäiskieli | Englanti |
---|---|
Sivut | 271–284 |
Sivumäärä | 14 |
Julkaisu | Discrete and Computational Geometry |
Vuosikerta | 61 |
Numero | 2 |
Varhainen verkossa julkaisun päivämäärä | 18 kesäk. 2018 |
DOI - pysyväislinkit | |
Tila | Julkaistu - 15 maalisk. 2019 |
OKM-julkaisutyyppi | A1 Julkaistu artikkeli, soviteltu |
Sormenjälki
Sukella tutkimusaiheisiin 'New Results on Tripod Packings'. Ne muodostavat yhdessä ainutlaatuisen sormenjäljen.Tietoaineistot
-
Dataset for New Results on Tripod Packings
Östergård, P. (Creator) & Pöllänen, A. (Creator), Zenodo, 26 huhtik. 2018
DOI - pysyväislinkki: 10.5281/zenodo.1230276
Tietoaineisto: Dataset
Projektit
- 1 Päättynyt
-
Konstruktion och klassificering av diskreta matematiska strukturer
Kokkala, J., Laaksonen, A., Östergård, P., Szollosi, F., Pöllänen, A., Ganzhinov, M. & Heinlein, D.
01/09/2015 → 31/08/2019
Projekti: Academy of Finland: Other research funding