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pro vyhledávání: '"RIPA, Marco"'
Autor:
Ripà, Marco
In the decimal numeral system, we prove that the well-known Graham's number, $G := \! ^{n}3$ (i.e., $3^{3^{\cdot^{\cdot^{\cdot^{3}}}}} n$-times), and any base $3$ tetration whose hyperexponent is larger than $n$ share the same $slog_3(G) - 1$ rightmo
Externí odkaz:
http://arxiv.org/abs/2411.00015
Autor:
Di Pietro, Gabriele, Ripà, Marco
For each pair of positive integers $(a,b)$ such that $a \geq 0$ and $b > 1$, the present paper provides a necessary and sufficient condition for the existence of Hamiltonian cycles visiting all the vertices of any $k$-dimensional grid $\{0,1\}^k \sub
Externí odkaz:
http://arxiv.org/abs/2409.03073
Autor:
Ripà, Marco
Publikováno v:
Notes on Number Theory and Discrete Mathematics, 20(1):59-71, 2014
A generalization of Rip\`a's square spiral solution for the $n \times n \times \cdots \times n$ Points Upper Bound Problem. Additionally, we provide a non-trivial lower bound for the $k$-dimensional $n_1 \times n_2 \times \cdots \times n_k$ Points Pr
Externí odkaz:
http://arxiv.org/abs/2409.02922
Autor:
Di Pietro, Gabriele, Ripà, Marco
The present paper aims to extend the knight's tour problem for $k$-dimensional grids of the form $\{0,1\}^k$ to other fairy chess leapers. Accordingly, we constructively show the existence of closed tours in $2 \times 2 \times \cdots \times 2$ ($k$ t
Externí odkaz:
http://arxiv.org/abs/2407.07903
Autor:
Ripà, Marco
For every non-negative integer $a$ and positive integer $b$, the congruence speed of the tetration $^{b}a$ is the difference between the number of the rightmost digits of $^{b}a$ that are the same as those of $^{b+1}a$ and the number of the rightmost
Externí odkaz:
http://arxiv.org/abs/2402.07929
Autor:
Ripà, Marco
Publikováno v:
Journal of Fundamental Mathematics and Applications, Vol. 4 (2021), No. 2, pp. 154-166
Given the finite set of $n_1 \cdot n_2 \cdot \ldots \cdot n_k$ points $G_{n_1,n_2,\ldots,n_k} \subset \mathbb{R}^k$ such that $n_k \geq \cdots \geq n_2 \geq n_1 \in \mathbb{Z}^+$, we introduce a new algorithm, called M$\Lambda$I, which returns an unc
Externí odkaz:
http://arxiv.org/abs/2402.00096
Autor:
Ripà, Marco
This paper aims to study the graph radii and diameters induced by the $k$-dimensional versions of the well-known six international chess pieces on every finite $\{n \times n \times \dots \times n\} \subseteq \mathbb{Z}^k$ lattice since they originate
Externí odkaz:
http://arxiv.org/abs/2311.00016
Autor:
Ripà, Marco
Publikováno v:
Notes on Number Theory and Discrete Mathematics, 30(1):20-33, 2024
The Knight's Tour problem consists of finding a Hamiltonian path for the knight on a given set of points so that the knight can visit exactly once every vertex of the mentioned set. In the present paper, we provide a $5$-dimensional alternative to th
Externí odkaz:
http://arxiv.org/abs/2309.09639
Autor:
Rinaldi, Roberto, Ripà, Marco
We solve the general problem of visiting all the $2^k$ nodes of a $k$-dimensional hypercube by using a polygonal chain that has minimum link-length, and we show that this optimal value is given by $h(2,k):=3 \cdot 2^{k-2}$ if and only if $k \in \math
Externí odkaz:
http://arxiv.org/abs/2212.11216
Autor:
Ripà, Marco, Onnis, Luca
Publikováno v:
Notes on Number Theory and Discrete Mathematics, 28(3):441-457, 2022
In the present paper we provide a formula that allows to compute the number of stable digits of any integer tetration base $a\in\mathbb{N}_0$. The number of stable digits, at the given height of the power tower, indicates how many of the last digits
Externí odkaz:
http://arxiv.org/abs/2210.07956