Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Przesławski, Krzysztof"'
Two axis-aligned boxes in $\mathbb{R}^d$ are \emph{$k$-neighborly} if their intersection has dimension at least $d-k$ and at most $d-1$. The maximum number of pairwise $k$-neighborly boxes in $\mathbb{R}^d$ is denoted by $n(k,d)$. It is known that $n
Externí odkaz:
http://arxiv.org/abs/2402.02199
A family of axis-aligned boxes in $\er^d$ is \emph{$k$-neighborly} if the intersection of every two of them has dimension at least $d-k$ and at most $d-1$. Let $n(k,d)$ denote the maximum size of such a family. It is known that $n(k,d)$ can be equiva
Externí odkaz:
http://arxiv.org/abs/2212.05133
We prove a combinatorial theorem on families of disjoint sub-boxes of a discrete cube, which implies that there are at most $2^{d+1}-2$ nearly neighbourly simplices in $\mathbb R^d$.
Comment: 6 pages, accepted to Discrete Comput. Geom
Comment: 6 pages, accepted to Discrete Comput. Geom
Externí odkaz:
http://arxiv.org/abs/1912.13176
Publikováno v:
In European Journal of Combinatorics December 2023 114
A combinatorial theorem on families of disjoint sub-boxes of a discrete cube, which implies that there at most $2^{d+1}-2$ neighbourly simplices in $\mathbb R^d$, is presented.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/1902.05597
Autor:
Przesławski, Krzysztof
Keller packings and tilings of boxes are investigated. Certain general inequality measuring a complexity of such systems is proved. A straightforward application to the unit cube tilings is given.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/1804.07499
It is demonstrated that each nearly neighbourly family of standard boxes in $\mathbb{R}^3$ has at most 12 elements. A combinatorial classification of all such families that have exactly 12 elements is given. All families satisfying an extra property
Externí odkaz:
http://arxiv.org/abs/1607.08195
Autor:
Przesławski, Krzysztof, Yost, David
We apply combinatorial methods to a geometric problem: the classification of polytopes, in terms of Minkowski decomposability. Various properties of skeletons of polytopes are exhibited, each sufficient to guarantee indecomposability of a significant
Externí odkaz:
http://arxiv.org/abs/1607.00643
It is shown that if n<7, then each tiling of R^n by translates of the unit cube [0,1)^n contains a column; that is, a family of the form {[0,1)^n+(s+ke_i): k \in Z}, where s \in R^n, e_i is an element of the standard basis of R^n and Z is the set of
Externí odkaz:
http://arxiv.org/abs/0809.1960
Let k_1,...,k_d be positive integers, and D be a subset of [k_1]x...x[k_d], whose complement can be decomposed into disjoint sets of the form {x_1}x...x{x_{s-1}}x[k_s]x{x_{s+1}}x...x{x_d}. We conjecture that the number of elements of D can be represe
Externí odkaz:
http://arxiv.org/abs/0807.0891