Tootfinder

Looking for Signs: Reasoning About FOBNNs Using SAT
Hans-J\"org Schurr, Ath\'ena\"is Vaginay
https://arxiv.org/abs/2506.19156 https://…

Looking for Signs: Reasoning About FOBNNs Using SAT
First-Order Boolean Networks with Non-deterministic updates (FOBNN) compute a boolean transition graph representing the absence and presence of species over time. The utility of FOBNNs has been justified by their theoretical soundness with respect to the Euler simulation of the differential equations. However, we lack practical means to work with FOBNNs and an empirical evaluation of their properties. We present a sound and efficient reduction of the first-order FOBNN transition relation to a p…

$p$-th order generalized Fibonacci cubes and maximal cubes in Fibonacci $p$-cubes
Michel Mollard (IF)
https://arxiv.org/abs/2507.16387 https://

$p$-th order generalized Fibonacci cubes and maximal cubes in Fibonacci $p$-cubes
The Fibonacci cube $Γ_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive 1s. We study a one parameter generalization, p-th order Fibonacci cubes $Γ^{(p)}_n$, which are subgraphs of $Q_n$ induced by strings without p consecutive 1s. We show the link between vertices of $Γ^{(p)}_n$ and compositions of integers with parts in $\{1, 2, \ldots , p\}$. Among other eumerative properties, we study the order, size and cube polynomial of $Γ^{(p)}_n$ as well as their gene…

On Pell numbers representable as product of two generalized Fibonacci numbers
Jhon J. Bravo, Pranabesh Das, Jose L. Herrera, John C. Saunders
https://arxiv.org/abs/2507.13674

On Pell numbers representable as product of two generalized Fibonacci numbers
A generalization of the well-known Fibonacci sequence is the $k$-Fibonacci sequence with some fixed integer $k\ge 2$. The first $k$ terms of this sequence are $0,0, \ldots, 1$, and each term afterwards is the sum of the preceding $k$ terms. In this paper, we find all Pell numbers that can be written as a product of two $k$-Fibonacci numbers. The proof of our main theorem uses lower bounds for linear forms in logarithms, properties of continued fractions, and a variation of a result of Dujella a…

Odd-indexed Fibonacci numbers via pattern-avoiding permutations
Juan B. Gil, Felix H. Xu, William Y. Zhu
https://arxiv.org/abs/2506.15800 https://

Odd-indexed Fibonacci numbers via pattern-avoiding permutations
In this paper, we consider several combinatorial problems whose enumeration leads to the odd-indexed Fibonacci numbers, including certain types of Dyck paths, block fountains, directed column-convex polyominoes, and set partitions with no crossings and no nestings. Our goal is to provide bijective maps to pattern-avoiding permutations and derive generating functions that track certain positional statistics at the permutation level.

People keep saying this and I remain mystified. It’s like I live in some different world.
Sure, getting a file to/from someone else is usually going to involve more faffing about but it’s still not likely going via email, and if all I need is to get it from one of my devices to another, that’s just trivial and *never* involves email.
Maybe a Windows or Android thing? Does Windows still not have built-in scp/sftp? Does Android not do SMB or DAV? Is it a skill issue?

🇺🇦 #NowPlaying on BBCRadio3's #Breakfast
Camille Saint‐Saëns, Louis Schwizgebel, BBC Symphony Orchestra & Fabien Gabel:
🎵 Piano Concerto no. 2 in G minor Op.22 - II: Allegro scherzando
#CamilleSaintSaëns #FabienGabel
https://open.spotify.com/track/4SDMUljWDMI8jKYZUIYIdq

Retention analysis of edited knowledge after fine-tuning
Fufang Wen, Shichang Zhang
https://arxiv.org/abs/2507.14198 https://arxiv.or…

Retention analysis of edited knowledge after fine-tuning
Large language models (LLMs) store vast amounts of knowledge, which often requires updates to correct factual errors, incorporate newly acquired information, or adapt model behavior. Model editing methods have emerged as efficient solutions for such updates, offering localized and precise knowledge modification at significantly lower computational cost than continual training. In parallel, LLMs are frequently fine-tuned for a wide range of downstream tasks. However, the effect of fine-tuning on…

Superconducting order parameter manifested in quasicrystals
Sougata Biswas, Debika Debnath, Paramita Dutta
https://arxiv.org/abs/2507.14671 https://…

Superconducting order parameter manifested in quasicrystals
Recent discovery of the superconducting ground state in Quasicrystals (QCs) has opened up an exciting new avenue for superconductivity based on QCs. However, theoretical studies to date have largely focused on a limited subset of quasiperiodic structures. In this work, we broaden the scope by theoretically investigating the behavior of the superconducting order parameter (OP) across a wide class of aperiodic systems, including both generalized Fibonacci and non-Fibonacci QCs based on the attrac…

Identically vanishing $k$-generalized Fibonacci polynomials
S. R. Mane
https://arxiv.org/abs/2507.11596 https://arxiv.org/pdf/2507.11…

Identically vanishing $k$-generalized Fibonacci polynomials
The Fibonacci polynomials are a generalization of the Fibonacci numbers. The $k$-generalized Fibonacci polynomials are a further generalization to $k\ge2$ summands, which satisfy the recurrence $\mathcal{F}_{n,k}(x) = x^{k-1}\mathcal{F}_{n-1,k}(x) +x^{k-2}\mathcal{F}_{n-2,k}(x) +\dots +\mathcal{F}_{n-k,k}(x)$. Most of the attention in the literature iterates the above recurrence upwards to positive values of $n$. We show that, when the recurrence is iterated downwards to negative values of $n$,…

Study of $p^{k}$-Eulerian polynomials and $p^{k}$-Fibonacci numbers for every odd prime $p$ and $k\geq0$
M. Parvathi, A. Tamilselvi, D. Hepsi
https://arxiv.org/abs/2506.09941

Study of $p^{k}$-Eulerian polynomials and $p^{k}$-Fibonacci numbers for every odd prime $p$ and $k\geq0$
In this paper, we define the notion of descent for the paths in the $p$-Bratteli diagram. This leads to the definition of $p^{k}$-Eulerian polynomials, whose coefficients count the number of paths with a given number of descents. We provide a method for constructing the $p^{k}$-Eulerian polynomials at each vertex. Furthermore, we compute the total number of descents of all paths ending at a given vertex as the corresponding $p^{k}$-Fibonacci numbers. We show that the derivative of the $p^{k}$-E…