arXiv subjects

Jinlong Tang

Publications and source records attributed to Jinlong Tang.

14 recordsLinked to original sources

arXiv2026

Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions

For a finite sequence of positive integers $\boldsymbol{a}=(a_1,\dots,a_n)$, the restricted partition function $q_{\boldsymbol{a}}(k)$ denote the number of nonnegative integer solutions to the equation $a_1x_1+a_2x_2+\cdots +a_nx_n=k$. It is proved to be a quasi-polynomial of degree $n-1$. Write $q_{\boldsymbol{a}}(k)=\sum_{j=0}^{n-1}c_j(k)k^j$ with periodic coefficient functions $c_j$, and set $b_m=\#\{i:m\mid a_i\}$. In 2008, Beck, Sam, and Woods conjectured that the minimum period of $c_j(k)$ is $\mathrm{lcm}\{m:b_m>j\}$. In this paper, we derive an exact root-of-unity formula for every coefficient function $c_j(k)$. The formula proves the conjectured divisibility upper bound, but it also reveals a lower bound for the period of $c_j(k)$. Both divisibility bounds are sharp. This leads us to construct a family of counterexamples to this conjecture.

math.CO↗

arXiv2026

Polynomial-Time Evaluation of Aardal-Lenstra Denumerants via Constant Term Method

Aardal and Lenstra systematically studied hard knapsack problems of the form $a_1x_1+\cdots+a_nx_n=b$, where $a_i=p_iM+r_iN$, $(M,N)$ is a coprime pair of positive integers, and the integers $|p_i|, |r_i|$ are small relative to $M$ and $N$. We investigate the corresponding challenging denumerant problem (i.e., counting the number of nonnegative integer solutions) and present a polynomial-time algorithm. This eliminates the computational bottlenecks caused by large values of $M$, $N$ and $b$. The proposed algorithm achieves a time complexity of $O(n^4\Delta^2\log n\log\Delta)$, which depends solely on the parameters $n$ and $\Delta=\max_{i,j}|r_i p_j - r_j p_i|$. Moreover, we consider the problem of expressing a general vector $(a_1,\dots,a_n)$ in the above form using the LLL algorithm.

math.CO↗

arXiv2026

Search for L4 Earth Trojan asteroids with the 2.5-meter Wide Field Survey Telescope

Earth Trojan asteroids (ETAs) are a mysterious population, and dynamically stable ETAs, if primordial, could be "living fossils" of the early solar system. To date, there are only two known ETAs, but both are temporary ETAs. The aim of our survey is to discover new temporary or stable ETAs; in the absence of detections, we derive upper limits on the population of stable ETAs. We conducted the largest wide-area survey of the Earth's L4 Lagrange point region so far using the Wide Field Survey Telescope, covering about 236.74 deg^2, corresponding to 33.24% of the probability coverage for sky regions where dynamically stable L4 ETAs are likely to reside. No new ETAs were detected in our survey. We place a cumulative upper limit of N(H < 19.1) < 19 on the stable population of objects larger than ~520 m (for an assumed albedo of 0.15). This represents the most stringent constraint on the ETA population to date.

astro-ph.EP↗

arXiv2026

Proofs of four generating function conjectures for arbor polytopes

This paper proves four conjectured generating series, due to Chapoton, which concern invariants of posets and polytopes associated with a specific sequence of arbors. Two of these conjectures provide closed-form formulas for the generating series of the Zeta polynomial and the generating series of the M-triangle of the poset, respectively. The remaining two conjectures pertain, respectively, to the Ehrhart polynomial and the Laplace transform of the volume function of the associated arbor polytope.

math.CO↗

arXiv2026

WFST Supernovae in the First Year: I. Statistical Study of 16 Early-phase Type Ia Supernovae from the Pilot Survey

In this paper we present 16 early-phase type Ia supernovae (SNe Ia) discovered during the pilot survey of the 2.5-meter Wide Field Survey Telescope (WFST-PS) from March 4 to July 10, 2024, including three SNe Ia with early-excess emission features (EExSNe Ia). The discovery magnitude of the 16 WFST-PS early-phase SNe is at least 3 mag fainter than their peak brightness. A large scatter of color indices is found in approximately the first 10 days of supernova explosions, indicating diverse photometric behaviors in the early phase. Three EExSNe Ia show relatively brighter peak luminosities and longer rise time compared to those of non-EExSNe Ia. The results indicate that current theoretical models require further refinement to fully capture the early photometric evolution of SNe Ia. Based on the initial high-cadence ugr-band data from the WFST-PS survey, we emphasize that early near-ultraviolet (NUV) observations are indispensable for placing tight constraints on the explosion mechanisms and progenitor systems of SNe Ia.

astro-ph.HE↗

arXiv2026

WFST Supernovae in the First Year: II. SN 2024aedt: Systematical Study of a Transitional Type Ia Supernova

We present comprehensive photometric and spectroscopic observations of a transitional type Ia SN 2024aedt, discovered by the 2.5-meter Wide Field Survey Telescope (WFST) within one day of the explosion. Its light curve is characterized by a peak absolute magnitude of $M_B = -18.49 \pm 0.03$ mag and a decline rate of $\Delta m_{15}(B) = 1.53 \pm 0.36$ mag, placing the object on the $\Delta m_{15}(B)$--$M_B$ diagram in the transition region between normal and subluminous SNe Ia. Furthermore, the early-color evolution and host galaxy environment of SN 2024aedt underscore its transitional nature, sharing properties with both normal and 91bg-like SNe Ia. Light-curve modeling with MOSFiT yields a synthesized $^{56}\mathrm{Ni}$ mass of $0.414 \pm 0.042\,M_{\odot}$ and a total ejecta mass of $0.548 \pm 0.108\,M_{\odot}$. A comparison with theoretical models suggests that the evolutionary trend can be broadly explained by both delayed-detonation (DDT) and double-detonation (DDet) scenarios while possible early-excess emissions predicted by DDet cannot be identified given the limited detections soon after the SN explosion. Although the overall spectral evolution of SN 2024aedt is similar to that of other transitional SNe Ia, the spectroscopic comparison reveals diversity in the early-phase blue-end features, which becomes more homogeneous at later phases. The result indicates the importance of early-time observations in understanding the origin of SN Ia diversity.

astro-ph.HE↗

arXiv2026

Illuminating the Mass Gap Through Deep Optical Constraint on a Neutron Star Merger Candidate S250206dm

The gravitational wave (GW) event S250206dm, as the first well-localized neutron star merger candidate potentially located in the mass gap, presented a unique opportunity to probe the electromagnetic signatures from such a system. Here we report a deep, multiband search with the new 2.5-meter Wide Field Survey Telescope (WFST), covering about 64% of the localization region up to a 5-sigma limiting magnitude of 23 mag. In total, 12 potential candidates have been identified while none of them are likely related to S250206dm. This non-detection provides the most stringent constraint to date on any associated kilonova. Crucially, an AT 2017gfo-like event at 269 Mpc can be excluded by WFST observations alone. Based on ejecta mass limits, a neutron star-black hole with a large mass ratio (Q >= 3.2) is disfavored. This optical-derived constraint on the mass ratio reaches, for the first time, a precision comparable to that inferred from the GW signal. This work presents the best observation of this type of events until now, and demonstrates the power of rapid, deep follow-up observations to constrain the properties of compact binary progenitors, offering key insights into the constituents of the mass gap.

astro-ph.HE↗

arXiv2025

TTC: Transformer-based TDE Classifier for the Wide Field Survey Telescope (WFST)

We propose the Transformer-based Tidal disruption events (TDE) Classifier (\texttt{TTC}), specifically designed to operate effectively with both real-time alert streams and archival data of the Wide Field Survey Telescope (WFST). It aims to minimize the reliance on external catalogs and find TDE candidates from pure light curves, which is more suitable for finding TDEs in faint and distant galaxies. \texttt{TTC} consists of two key modules that can work independently: (1) A light curve parametric fitting module and (2) a Transformer (\texttt{Mgformer})-based classification network. The training of the latter module and evaluation for each module utilize a light curve dataset of 7413 spectroscopically classified transients from the Zwicky Transient Facility (ZTF). The \texttt{Mgformer}-based module is superior in performance and flexibility. Its representative recall and precision values are 0.79 and 0.76, respectively, and can be modified by adjusting the threshold. It can also efficiently find TDE candidates within 30 days from the first detection. For comparison, the parametric fitting module yields values of 0.72 and 0.40, respectively, while it is $>$10 times faster in average speed. Hence, the setup of modules allows a trade-off between performance and time, as well as precision and recall. \texttt{TTC} has successfully picked out all spectroscopically identified TDEs among ZTF transients in a real-time classification test, and selected $\sim$20 TDE candidates in the deep field survey data of WFST. The discovery rate will greatly increase once the differential database for the wide field survey is ready.

astro-ph.IM↗

arXiv2025

A Star's Death by a Thousand Cuts: The Runaway Periodic Eruptions of AT2023uqm

Stars on bound orbits around a supermassive black hole may undergo repeated partial tidal disruption events (rpTDEs), producing periodic flares. While several candidates have been suggested, definitive confirmation of these events remains elusive. We report the discovery of AT2023uqm, a nuclear transient that has exhibited at least five periodic optical flares, making it only the second confirmed case of periodicity after ASASSN-14ko. Uniquely, the flares from AT2023uqm show a nearly exponential increase in energy--a "runaway" phenomenon signaling the star's progressive destruction. This behavior is consistent with rpTDEs of low-mass, main-sequence stars or evolved giant stars. Multiwavelength observations and spectroscopic analysis of the two most recent flares reinforce its interpretation as an rpTDE. Intriguingly, each flare displays a similar double-peaked structure, potentially originating from a double-peaked mass fallback rate or two discrete collisions per orbit. The extreme ratio of peak separation to orbital period draws attention to the possibility of a giant star being disrupted, which could be distinguished from a low-mass main-sequence star by its future mass-loss evolution. Our analysis demonstrates the power of rpTDEs to probe the properties of disrupted stars and the physical processes of tidal disruption, though it is currently limited by our knowledge of these events. AT2023uqm emerges as the most compelling rpTDE thus far, serving as a crucial framework for modeling and understanding these phenomena.

astro-ph.HE↗

arXiv2025

A Glimpse of Satellite Galaxies in the Milky Way with the 2.5-meter Wide Field Survey Telescope (WFST): Bootes III and Draco

We carry out deep imaging of the Milky Way satellite galaxies, Bootes III and Draco, with WFST as one pilot observing program to demonstrate the capability of WFST. Combining catalogs with PS1 DR2 and Gaia DR3, we derive proper motions for candidate member stars in these two satellite galaxies over a 12-year time baseline, yielding uncertainties of ~1.8 mas/yr at 21 mag and ~3.0 mas/yr at 22 mag in the r band. The proper motions derived from bright and faint stars are consistent, indicating no significant variation in proper motion across stellar luminosity as these galaxies undergo tidal interactions with the MW. Meanwhile, we suggest that Bootes III represents the bound remnant of the progenitor galaxy that gave rise to the Styx stream, as evidenced by its elongated density profile and overdensity in both spatial and kinematic space. This is the first paper to use WFST to measure the proper motions of faint stars in Milky Way satellite galaxies. More detailed analyses will be presented in forthcoming papers from the wide field survey (WFS) program.

astro-ph.GA↗

arXiv2025

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle

This paper resolves an open problem raised by Ekhad and Zeilberger for computing $\omega(10000)$, which is related to Stern's triangle. While $\nu(n)$, defined as the sum of squared coefficients in $\prod_{i=0}^{n-1} (1 + x^{2^i} + x^{2^{i+1}})$, admits a rational generating function, the analogous function $\omega(n)$ for $\prod_{i=0}^{n-1} (1 + x^{2^i+1} + x^{2^{i+1}+1})$ presents substantial computational difficulties due to its complex structure. We develop a method integrating constant term techniques, conditional transfer matrices, algebraic generating functions, and $P$-recursions. Using the conditional transfer matrix method, we represent $\omega(n)$ as the constant term of a bivariate rational function. This framework enables the calculation of $\omega(10000)$, a $6591$-digit number, and illustrates the method's broad applicability to combinatorial generating functions.

math.CO↗

arXiv2025

A pilot survey on globular clusters with the Wide Field Survey Telescope (WFST)

We carry out an imaging survey of six globular clusters (GCs) with a limit magnitude to 22 mag at the 5 sigma level, down to the main sequence stars of the respective cluster, as one of the pilot observing program of the Wide Field Survey Telescope (WFST). This paper present the early results of this survey, where we investigate the tidal characters at the periphery of the clusters NGC 4147, NGC 5024, NGC 5053, NGC 5272, NGC 5904 and NGC 6341. We present the estimated number density of cluster candidates and their spatial distribution. We confirm the presence of tidal arms in NGC 4147 and NGC 5904 and identify several intriguing potential tidal structures in NGC 4147, NGC 5024, NGC 5272, corroborated the elliptical morphology of the periphery of NGC 6341. WFST shows its ability to detect faint main-sequence stars of clusters beyond 15 kpc in helio-centric distance. Our findings underscore the WFST's capability for probing faint structural features in GCs, paving the way for future in-depth studies, especially for the search of the large scale tidal streams associated with the clusters with the future wide field survey.

astro-ph.GA↗

arXiv2024

Minute-cadence observations on Galactic plane with Wide Field Survey Telescope (WFST): Overview, methodology and early results

As the time-domain survey telescope of the highest survey power in the northern hemisphere currently, Wide Field Survey Telescope (WFST) is scheduled to hourly/daily/semi-weekly scan northern sky up to ~23 mag in four optical (ugri) bands. Unlike the observation cadences in the forthcoming regular survey missions, WFST performed "staring" observations toward Galactic plane in a cadence of $\approx$1 minute for a total on-source time of about 13 hours, during the commissioning and pilot observation phases. Such an observation cadence is well applied in producing densely sampling light curves and hunting for stars exhibiting fast stellar variabilities. Here we introduce the primary methodologies in detecting variability, periodicity, and stellar flares among a half million sources from the minute-cadence observations, and present the WFST g-/r-band light curves generated from periodic variable stars and flaring stars. Benefit from high photometric precisions and deep detection limits of WFST, the observations have captured several rare variable stars, such as a variable hot white dwarf (WD) and an ellipsoidal WD binary candidate. By surveying the almost unexplored parameter spaces for variables, WFST will lead to new opportunities in discovering unique variable stars in the northern sky.

astro-ph.SR↗

arXiv2024

AT2023lli: A Tidal Disruption Event with Prominent Optical Early Bump and Delayed Episodic X-ray Emission

High-cadence, multiwavelength observations have continuously revealed the diversity of tidal disruption events (TDEs), thus greatly advancing our knowledge and understanding of TDEs. In this work, we conducted an intensive optical-UV and X-ray follow-up campaign of TDE AT2023lli, and found a remarkable month-long bump in its UV/optical light curve nearly two months prior to maximum brightness. The bump represents the longest separation time from the main peak among known TDEs to date. The main UV/optical outburst declines as $t^{-4.10}$, making it one of the fastest decaying optically selected TDEs. Furthermore, we detected sporadic X-ray emission 30 days after the UV/optical peak, accompanied by a reduction in the period of inactivity. It is proposed that the UV/optical bump could be caused by the self-intersection of the stream debris, whereas the primary peak is generated by the reprocessed emission of the accretion process. In addition, our results suggest that episodic X-ray radiation during the initial phase of decline may be due to the patched obscurer surrounding the accretion disk, a phenomenon associated with the inhomogeneous reprocessing process. The double TDE scenario, in which two stars are disrupted in sequence, is also a possible explanation for producing the observed early bump and main peak. We anticipate that the multicolor light curves of TDEs, especially in the very early stages, and the underlying physics can be better understood in the near future with the assistance of dedicated surveys such as the deep high-cadence survey of the 2.5-meter Wide Field Survey Telescope (WFST).

astro-ph.HE↗