Tootfinder

On the arithmetic properties of partitions into parts simultaneously $4$-regular and $9$-distinct
Mohammed L. Nadji, Moussa Ahmia
https://arxiv.org/abs/2506.07704

On the arithmetic properties of partitions into parts simultaneously $4$-regular and $9$-distinct
In 2017, Keith presented a comprehensive survey on integer partitions into parts that are simultaneously regular, distinct, and/or flat. Recently, the authors initiated a study of partitions into parts that are simultaneously regular and distinct, examining them from both arithmetic and combinatorial perspectives. In particular, several Ramanujan-like congruences were obtained for $\myRD^{(\ell, t)}(n)$, the number of partitions of $n$ into parts that are simultaneously $\ell$-regular and $t$-d…

The combinatorics of partition identities in Andrews and Bachraoui's paper
Haijun Li
https://arxiv.org/abs/2506.06640 https://arx…

The combinatorics of partition identities in Andrews and Bachraoui's paper
Recently, Andrews and Bachraoui discovered several companions for some famous $q$-series formulas, and derived some now identities involving partitions and overpartitions. In this paper, we shall refine their partial results by the number of parts of partitions and furthermore, we also give the combinatorial proofs for those identities.

Hermeus' Prototyp Quarterhorse Mk 1 fliegt erstmals
Das US-Luftfahrtunternehmen Hermeus will Hyperschallflugzuge bauen. Der Prototyp Quarterhorse Mk 1 hat seinen Erstflug absolviert.
https://www.

Correcting Errors Through Partitioning and Burst-Deletion Correction
Yubo Sun, Gennian Ge
https://arxiv.org/abs/2506.07609 https://ar…

Correcting Errors Through Partitioning and Burst-Deletion Correction
In this paper, we propose a partitioning technique that decomposes a pair of sequences with overlapping $t$-deletion $s$-substitution balls into sub-pairs, where the $^{\leq}t$-burst-deletion balls of each sub-pair intersect. This decomposition facilitates the development of $t$-deletion $s$-substitution correcting codes that leverage approaches from $^{\leq}t$-burst-deletion correction. Building upon established approaches in the $^{\leq}t$-burst-deletion correction domain, we construct $t$-de…

Quasinormal bulk-edge characters of gravitons in Nariai geometry
Jyotirmoy Mukherjee
https://arxiv.org/abs/2506.07556 https://arxiv.o…

Quasinormal bulk-edge characters of gravitons in Nariai geometry
In this paper, we evaluate the character partition function of gravitons in the Nariai geometry using quasinormal modes. Employing the Denef-Hartnoll-Sachdev (DHS) prescription, we compute the bulk partition function from the spectrum of quasinormal frequencies. We demonstrate that the quasinormal partition function agrees with the bulk one-loop determinant of gravitons on $S^2 \times S^2$, as obtained via the heat kernel method. Furthermore, we isolate the contribution of the edge character fr…

100,000 Crab giant pulses at 215 MHz detected with an SKA-Low prototype station
M. Sokolowski, P. Kumar, S. Dhavali, B. W. Meyers, N. D. R. Bhat, A. Bera, S. McSweeney
https://arxiv.org/abs/2506.07422

100,000 Crab giant pulses at 215 MHz detected with an SKA-Low prototype station
We report detection and analysis of the largest low-frequency (200 - 231.25 MHz) sample of Crab giant pulses (GPs) reported in the literature. In total about 95000 GPs were detected. The observations were performed in 2024/2025 with the EDA2, a prototype station of the SKA-Low telescope. The fluence distribution of GPs in the entire sample is very well characterised with a single power law (no flattening at higher fluences) N(F) $\propto$ F$^α$, where $α= -3.17\pm0.02$ for all GPs, and $α_{M…

This https://arxiv.org/abs/2504.17928 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Energy partitioning between thermal and non-thermal electrons and ions in magnetotail reconnection
Magnetic reconnection is an explosive energy release event. It plays an important role in accelerating particles to high non-thermal energies. These particles often exhibit energy spectra characterized by a power-law distribution. However, the partitioning of energy between thermal and non-thermal components, and between ions and electrons, remains unclear. This study provides estimates of energy partition based on a statistical analysis of magnetic reconnection events in Earth's magnetotail us…

Periodicity in delayed self-regulation is a predator-prey process
Alejandro L\'opez-Nieto
https://arxiv.org/abs/2506.07660 https://

Periodicity in delayed self-regulation is a predator-prey process
We unify two different periodicity mechanisms: delayed self-regulation and planar predator-prey feedback. We consider scalar delay differential equations $\dot x(t) = rf(x(t), x(t - 1))$ where $f$ is monotone in the delayed component. Due to a Poincaré--Bendixson theorem for monotone delayed feedback systems, the typical global dynamics present periodic orbits as the delay parameter $r$ increases. In this article, we show that, as we vary the delay, each connected component of periodic orbits …

Ramanujan's partition generating functions modulo $\ell$
Kathrin Bringmann, William Craig, Ken Ono
https://arxiv.org/abs/2506.06101 https://

Ramanujan's partition generating functions modulo $\ell$
For the partition function $p(n)$, Ramanujan proved the striking identities $$ P_5(q):=\sum_{n\geq 0} p(5n+4)q^n =5\prod_{n\geq 1} \frac{\left(q^5;q^5\right)_{\infty}^5}{(q;q)_{\infty}^6}, $$ $$ P_7(q):=\sum_{n\geq 0} p(7n+5)q^n =7\prod_{n\geq 1}\frac{\left(q^7;q^7\right)_{\infty}^3}{(q;q)_{\infty}^4}+49q \prod_{n\geq 1}\frac{\left(q^7;q^7\right)_{\infty}^7}{(q;q)_{\infty}^8}, $$ where $(q;q)_{\infty}:=\prod_{n\geq 1}(1-q^n).$ As these identities imply his celebrated congruences modulo 5 …

This https://arxiv.org/abs/2502.07995 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Genuine multi-entropy and holography
Is bipartite entanglement sufficient for holography? Through the analysis of the Markov gap, it is known that the answer is no. In this paper, we give a new perspective on this issue from a different angle using a multi-entropy. We define a genuine $\mathtt{q}$-partite multi-entropy from a $\mathtt{q}$-partite multi-entropy by subtracting appropriate linear combinations of $\mathtt{\tilde{q}}$-partite multi-entropies for $\mathtt{\tilde{q}} < \mathtt{q}$, in such a way that the genuine $\mathtt…