Tootfinder

This https://arxiv.org/abs/1904.12500 has been replaced.
link: https://scholar.google.com/scholar?q=a

Composing dynamic programming tree-decomposition-based algorithms
Given two integers $\ell$ and $p$ as well as $\ell$ graph classes $\mathcal{H}_1,\ldots,\mathcal{H}_\ell$, the problems $\mathsf{GraphPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell,p)$, \break $\mathsf{VertPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell)$, and $\mathsf{EdgePart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell)$ ask, given graph $G$ as input, whether $V(G)$, $V(G)$, $E(G)$ respectively can be partitioned into $\ell$ sets $S_1, \ldots, S_\ell$ such that, for each $i$ between $1$ and $\ell$,…

🔊 #NowPlaying on KEXP's #AfternoonShow
Lætitia Sadier:
🎵 La Nageuse Nue
#LætitiaSadier
https://open.spotify.com/track/47orBvN9aVksNz6ttRB5rF
https://laetitiasadier.bandcamp.com/track/la-nageuse-nue

This https://arxiv.org/abs/2404.06598 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Extremes of generalized inversions on symmetric groups
The classical inversion statistic on symmetric groups is the sum of all indicators $\textbf{1}\{π(i) > π(j)\}$ for a random permutation $π= (π(1), \ldots, π(n))$ and the pairs $(i,j)$ with $1 \leq i < j \leq n$. The descent statistic counts all $i \in \{1, \ldots, n-1\}$ with $π(i) > π(i+1)$. The number of inversions can be generalized by restricting the indicators to pairs $(i,j)$ with $i

🔊 #NowPlaying on KEXP's #VarietyMix
Lætitia Sadier:
🎵 Don’t Forget You’re Mine
#LætitiaSadier
https://open.spotify.com/track/2vMzXeuXwbInPyLJtfOQyV
https://laetitiasadier.bandcamp.com/track/don-t-forget-you-re-mine

«A glimpse of an alternative economic and industrial history and future, in which the Luddites were successful in their battle against alienating technology.»
https://thereader.mitpress.mit.edu/the-future-encyclopedia-of-luddism/

PrivFED -- A Framework for Privacy-Preserving Federated Learning in Enhanced Breast Cancer Diagnosis
Maithili Jha, S. Maitri, M. Lohithdakshan, Shiny Duela J, K. Raja
https://arxiv.org/abs/2405.08084

This https://arxiv.org/abs/2404.06951 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Explicit lower bound for large gaps between some consecutive primes
Let $p_{n}$ denote the $n$th prime and for any fixed positive integer $k$ and $X\geq 2$, put \[ G_{k}(X):=\max _{p _{n+k}\leq X} \min \{ p_{n+1}-p_{n}, \ldots , p_{n+k}-p_{n+k-1} \}. \] Ford, Maynard and Tao proved that there exists an effective abosolute constant $c_{LG}>0$ such that \[ G_{k}(X)\geq \frac{c_{LG}}{k^{2}}\frac{\log X \log \log X \log \log \log \log X}{\log \log \log X} \] holds for any sufficiently large $X$. The main purpose of this paper is to determine the constant $c_{LG}$ a…

On set systems with strongly restricted intersections
Xin Wei, Xiande Zhang, Gennian Ge
https://arxiv.org/abs/2404.08280 https://arxi…

On set systems with strongly restricted intersections
Set systems with strongly restricted intersections, called $α$-intersecting families for a vector $α$, were introduced recently as a generalization of several well-studied intersecting families including the classical oddtown and eventown. Given a binary vector $α=(a_1, \ldots, a_k)$, a collection $\mathcal F$ of subsets over an $n$ element set is an $α$-intersecting family modulo $2$ if for each $i=1,2,\ldots,k$, all $i$-wise intersections of distinct members in $\mathcal F$ have sizes wit…

This https://arxiv.org/abs/2306.02721 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Alternating Parity Weak Sequencing
A subset $S$ of a group $(G,+)$ is $t$-weakly sequenceable if there is an ordering $(y_1, \ldots, y_k)$ of its elements such that the partial sums~$s_0, s_1, \ldots, s_k$, given by $s_0 = 0$ and $s_i = \sum_{j=1}^i y_j$ for $1 \leq i \leq k$, satisfy $s_i \neq s_j$ whenever and $1 \leq |i-j|\leq t$. In [10] it was proved that if the order of a group is $pe$ then all sufficiently large subsets of the non-identity elements are $t$-weakly sequenceable when $p > 3$ is prime, $e \leq 3$ …

Simplified Tight Bounds for Monotone Minimal Perfect Hashing
Dmitry Kosolobov
https://arxiv.org/abs/2403.07760 https://arxiv.org/pdf/…

Simplified Tight Bounds for Monotone Minimal Perfect Hashing
Given an increasing sequence of integers $x_1,\ldots,x_n$ from a universe $\{0,\ldots,u-1\}$, the monotone minimal perfect hash function (MMPHF) for this sequence is a data structure that answers the following rank queries: $rank(x) = i$ if $x = x_i$, for $i\in \{1,\ldots,n\}$, and $rank(x)$ is arbitrary otherwise. Assadi, Farach-Colton, and Kuszmaul recently presented at SODA'23 a proof of the lower bound $Ω(n \min\{\log\log\log u, \log n\})$ for the bits of space required by MMPHF, provided …