Tootfinder

Entropy Bounds for Perfect Matchings in Bipartite Hypergraphs
Tantan Dai, Alexander Divoux, Tom Kelly
https://arxiv.org/abs/2506.17652 https://

Entropy Bounds for Perfect Matchings in Bipartite Hypergraphs
A hypergraph is \textit{bipartite with bipartition} $(A, B)$ if every edge has exactly one vertex in $A$, and a matching in such a hypergraph is \textit{$A$-perfect} if it saturates every vertex in $A$. We prove an upper bound on the number of $A$-perfect matchings in uniform hypergraphs with small maximum codegree. Using this result, we prove that there exist order-$n$ Latin squares with at most $(n/e^{2.117})^n$ transversals when $n$ is odd and $n \equiv 0\pmod 3$. We also show that $k$-unifo…

Robustness of Majorana modes to potential disorder in Fe chains on a superconducting Rashba alloy
Harim Jang, Daniel Crawford, Khai Ton That, Lucas Schneider, Jens Wiebe, Makoto Shimizu, Harald O. Jeschke, Stephan Rachel, Roland Wiesendanger
https://arxiv.org/abs/2506.17414

Robustness of Majorana modes to potential disorder in Fe chains on a superconducting Rashba alloy
Majorana modes offer great potential for fault-tolerant quantum computation due to their topological protection. However, for superconductor-semiconductor nanowire hybrids, intrinsic disorder makes the unambiguous detection of Majorana modes difficult. Here, we construct 1D spin chains from individual Fe atoms on the Rashba surface alloy BiAg2/Ag(111) with proximity-induced superconductivity from a Nb(110) substrate. While the Fe chains exhibit perfect crystalline order, we observe nano-scale p…

Factorization and Resummation for the Nearside Energy-Energy Correlators
Yuxun Guo, Feng Yuan, Wenbin Zhao
https://arxiv.org/abs/2507.15820 https://…

Factorization and Resummation for the Nearside Energy-Energy Correlators
By utilizing the di-hadron fragmentation formalism, we extend the previous factorization of nearside energy-energy correlators (EEC) in the collinear limit and derive an all order resummation in the Fourier transform $b_T$-space. A perfect matching is obtained when we compare to the fixed-order results. We further demonstrate the resummation effects for the EEC in $e^+e^-$ annihilation and show that they will significantly improve the theoretical predictions at small angles.

Discrete time crystal and perfect many-body tunneling in a periodically driven Heisenberg spin chain
Xiaotong Chen, Jianda Wu
https://arxiv.org/abs/2507.15565

Discrete time crystal and perfect many-body tunneling in a periodically driven Heisenberg spin chain
We investigate the non-equilibrium dynamics of a Heisenberg spin-1/2 chain driven by a periodic magnetic field. Based on its instantaneous integrability and inherent symmetry, we analytically study the magnetization and many-body tunneling (MBT). Both of them exhibit periodicity distinct from the driving period. The magnetization is shown to be independent of the initial state and robust against perturbations, signaling the formation of discrete time crystal (DTC) order. The DTC phase is found …

High-post-Newtonian-order dynamical effects induced by tail-of-tail interactions in a two body system
Donato Bini, Thibault Damour, Andrea Geralico
https://arxiv.org/abs/2507.08708

High-post-Newtonian-order dynamical effects induced by tail-of-tail interactions in a two body system
Starting from the recently derived conservative tail-of-tail action [D. Bini and T. Damour, arXiv:2504.20204 [hep-th]] we compute several dynamical observables of binary systems (Delaunay Hamiltonian, scattering angle), at the 6.5 post-Newtonian accuracy and up to the 8th post-Minkowskian order. We find perfect agreement with previous self-force results, and (when inserting a recent high-post-Newtonian order derivation of radiated angular momentum [A. Geralico, arXiv:2507.03442 [gr-qc]]) with s…

An Equivalent Representation of Generalized Differentials
Valentin Suder
https://arxiv.org/abs/2507.07337 https://arxiv.org/pdf/2507.…

An Equivalent Representation of Generalized Differentials
We propose an equivalent formula for the higher-order derivatives used in the study of Generalized Almost Perfect Nonlinear functions over an arbitrary finite field of characteristic $p$. The result is obtained by counting the number of subsets of the prime field with a fixed cardinality for which the sum of their elements is constant. We then ask related questions regarding the diversity of higher-order derivatives.

Perfect $1$-factorisations of $K_{11,11}$
Jack Allsop, Ian M. Wanless
https://arxiv.org/abs/2506.02455 https://arxiv.org/pdf/2506.024…

Perfect $1$-factorisations of $K_{11,11}$
A perfect $1$-factorisation of a graph is a decomposition of that graph into $1$-factors such that the union of any two $1$-factors is a Hamiltonian cycle. A Latin square of order $n$ is row-Hamiltonian if for every pair $(r,s)$ of distinct rows, the permutation mapping $r$ to $s$ has a single cycle of length $n$. We report the results of a computer enumeration of the perfect $1$-factorisations of the complete bipartite graph $K_{11,11}$. This also allows us to find all row-Hamiltonian Latin sq…

This https://arxiv.org/abs/2503.00817 has been replaced.
initial toot: https://mastoxiv.page/@…

Uniaxial Ordering by Self-Assembly of Isotropic Octahedral Junctions
We demonstrate that isotropic octahedral (sixfold branched) junctions with three diagonal endpoint pairs of different colors almost inevitably form a macroscopic assembly of uniaxial order, exhibiting the perfect order of a single color. Monte Carlo simulations of the antiferromagnetic three-state Potts model on the tripartite reo net, consisting of corner-sharing regular octahedrons, confirm this counterintuitive prediction, while showcasing switching self-assembly upon an ordering phase trans…