Andrzej P. Kisielewicz

activity

20232026

collaborators

6 papers

math.CO2026

Cube tilings, partition counters, and the Calkin--Wilf and Kepler trees

Jarosław Grytczuk, Andrzej P. Kisielewicz, Krzysztof Przesławski

A tiling of the integer lattice $Z^{d}$ by translates of the discrete cube $K_{d} = {0, 1}^{d}$ cuts every translate $K_{d} + x$ into subcubes. We study the function $ℓ (x)$ counti…

math.CO2026

Local fluctuations, majorization, and nontransitivity in cube tilings of $Z^{d}$

Andrzej P. Kisielewicz

Let $P$ be a partition of $Z^{d}$ into translates of the discrete unit cube ${0, 1}^{d}$ . For a uniformly chosen $ε \in {0, 1}^{d}$ , we count the cubes of $\…

math.CO2025

Neighborly boxes and strings with jokers; constructions and asymptotics

Jarosław Grytczuk, Andrzej P. Kisielewicz, Krzysztof Przesławski

We study families of axis-aligned boxes in a $d$ -dimensional Euclidean space $R^{d}$ whose placement is restricted by bounds on the dimension of their pairwise intersections…

math.CO2024

Neighborly boxes and bipartite coverings; constructions and conjectures

Jarosław Grytczuk, Andrzej P. Kisielewicz, Krzysztof Przesławski

Two axis-aligned boxes in $R^{d}$ are \emph{ $k$ -neighborly} if their intersection has dimension at least $d - k$ and at most $d - 1$ . The maximum number of pairwise $k$ -neighbor…

math.CO2024

A note on a flip-connected class of generalized domino tilings of the box $[0, 2]^{n}$

Andrzej P. Kisielewicz

Let $n, d \in N$ and $n > d$ . An $(n - d)$ -domino is a box $I_{1} \times \dots \times I_{n}$ such that $I_{j} \in {[0, 1], [1, 2]}$ for all $j \in N \subset [n]$ with $∣ N ∣ = d$ and $I_i=[0,…

math.CO2023

On the number of neighborly simplices in R^d

Andrzej P. Kisielewicz

Two $d$ -dimensional simplices in $R^{d}$ are neighborly if its intersection is a $(d - 1)$ -dimensional set. A family of $d$ -dimensional simplices in $R^{d}$ is called neighborly if every…

Cube tilings, partition counters, and the Calkin--Wilf and Kepler trees

Local fluctuations, majorization, and nontransitivity in cube tilings of Zd

Neighborly boxes and strings with jokers; constructions and asymptotics

Neighborly boxes and bipartite coverings; constructions and conjectures

A note on a flip-connected class of generalized domino tilings of the box [0,2]n

On the number of neighborly simplices in R^d

Local fluctuations, majorization, and nontransitivity in cube tilings of $Z^{d}$

A note on a flip-connected class of generalized domino tilings of the box $[0, 2]^{n}$