Zobrazeno 1 - 10
of 278
pro vyhledávání: '"Ripa, Marco"'
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
Autor:
Ripà, Marco
Publikováno v:
Notes on Number Theory and Discrete Mathematics, 27(4):43-61, 2021
We solve a few open problems related to a peculiar property of the integer tetration ${^{b}a}$, which is the constancy of its congruence speed for any sufficiently large $b=b(a)$. Assuming radix-$10$ (the well-known decimal numeral system), we provid
Externí odkaz:
http://arxiv.org/abs/2208.02622
Autor:
Ripà, Marco
Given any $n \in \mathbb{Z}^{+}$, we constructively prove the existence of covering paths and circuits in the plane which are characterized by the same link length of the minimum-link covering trails for the two-dimensional grid $G_n^2 := \{0,1, \ldo
Externí odkaz:
http://arxiv.org/abs/2207.08708
Autor:
Ripà, Marco
In 1994, Kranakis et al. published a conjecture about the minimum link-length of every rectilinear covering path for the $k$-dimensional grid $P(n,k) := \{0,1, \dots, n-1\} \times \{0,1, \dots, n-1\} \times \cdots \times \{0,1, \dots, n-1\}$. In this
Externí odkaz:
http://arxiv.org/abs/2208.01699