Zobrazeno 1 - 10
of 250 665
pro vyhledávání: '"P. LUCAS"'
Autor:
Mollard, Michel
The Fibonacci-run graphs $\mathcal{R}_n$ are a family of an induced subgraph of hypercubes introduced by E\u{g}ecio\u{g}lu and Ir\v{s}i\v{c} in 2021. A cyclic version of $\mathcal{R}_n$, the Lucas-run graph $\mathcal{R}_n^l$, was also recently propos
Externí odkaz:
http://arxiv.org/abs/2410.19326
Autor:
Da Conceição, Joaquim Cera
It is known that all terms $U_n$ of a classical regular Lucas sequence have a primitive prime divisor if $n>30$. In addition, a complete description of all regular Lucas sequences and their terms $U_n$, $2\leq n\leq 30$, which do not have a primitive
Externí odkaz:
http://arxiv.org/abs/2410.04957
Autor:
Batte, Herbert, Luca, Florian
Let $(L_n^{(k)})_{n\geq 2-k}$ be the sequence of $k$--generalized Lucas numbers for some fixed integer $k\ge 2$ whose first $k$ terms are $0,\ldots,0,2,1$ and each term afterwards is the sum of the preceding $k$ terms. In this paper, we completely so
Externí odkaz:
http://arxiv.org/abs/2412.12130
Autor:
Schenke, Maximilian, Bukarov, Shalbus
The discipline of automatic control is making increased use of concepts that originate from the domain of machine learning. Herein, reinforcement learning (RL) takes an elevated role, as it is inherently designed for sequential decision making, and c
Externí odkaz:
http://arxiv.org/abs/2412.02264
Autor:
Da Conceição, Joaquim Cera
Publikováno v:
J. Integer Sequences 26 (2023) Article 23.9.7
We define a new generalization of Catalan numbers to multinomial coefficients. With arithmetic methods, we study their integrality and the integrality of their Lucasnomial generalization. We give a complete characterization of regular Lucas sequences
Externí odkaz:
http://arxiv.org/abs/2410.04857
Autor:
Mandal, Priyabrata
This paper explores the intricate relationships between Lucas numbers and Diophantine equations, offering significant contributions to the field of number theory. We first establish that the equation regarding Lucas number $L_n = 3x^2$ has a unique s
Externí odkaz:
http://arxiv.org/abs/2409.10152
Autor:
O'Rourke, Sean, Williams, Noah
If $p:\mathbb{C} \to \mathbb{C}$ is a non-constant polynomial, the Gauss--Lucas theorem asserts that its critical points are contained in the convex hull of its roots. We consider the case when $p$ is a random polynomial of degree $n$ with roots chos
Externí odkaz:
http://arxiv.org/abs/2409.09538
Autor:
Mu, Weihua, Cao, Lina
This study extends the Lucas-Washburn theory through non-equilibrium thermodynamic analysis to examine fluid absorption in medical foams used for hemorrhage control. As a universal model for capillary flow in porous media, the theory demonstrated str
Externí odkaz:
http://arxiv.org/abs/2409.06265
In this work, we prove that many Ap\'ery-like sequences arising from modular forms satisfy the Lucas congruences modulo any prime. As an implication, we completely affirm four conjectural Lucas congruences that were recently posed by S. Cooper and re
Externí odkaz:
http://arxiv.org/abs/2408.16616
The goal of this paper is twofold: (1) extend theory on certain statistics in the Fibonacci and Lucas sequences modulo $m$ to the Lucas sequences $U := \left(U_n(p,q)\right)_{n \geq 0}$ and $V := \left(V_n(p,q)\right)_{n \geq 0}$, and (2) apply some
Externí odkaz:
http://arxiv.org/abs/2408.14632