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Researcher profile

Jianping Pan

Jianping Pan contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.COMachine Learningmath.GMmath.QA

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Published work

6 published item(s)

preprint2026arXiv

Hook-valued tableau uncrowding and tableau switching

Refined canonical stable Grothendieck polynomials were introduced by Hwang, Jang, Kim, Song, and Song. There exist two combinatorial models for these polynomials: one using hook-valued tableaux and the other using pairs of a semistandard Young tableau and (what we call) an exquisite tableau. An uncrowding algorithm on hook-valued tableaux was introduced by Pan, Pappe, Poh, and Schilling. In this paper, we discover a novel connection between the two models via the uncrowding and Goulden--Greene's jeu de taquin algorithms, using a classical result of Benkart, Sottile, and Stroomer on tableau switching. This connection reveals a symmetry of the uncrowding algorithm defined on hook-valued tableaux. As a corollary, we obtain another combinatorial model for the refined canonical stable Grothendieck polynomials in terms of biflagged tableaux, which naturally appear in the characterization of the image of the uncrowding map.

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preprint2026arXiv

Worst-Case Regret Bounds for Combinatorial Thompson Sampling in Sleeping Semi-Bandits

We revisit combinatorial Thompson sampling (CTS) for semi-bandits with sleeping arms, where arm availability varies over time and actions must satisfy combinatorial constraints, as in wireless mesh routing with fluctuating link availability. Despite its practical relevance, CTS has been hindered by several long-standing problems: (i) the absence of worst-case regret guarantees in the semi-bandit setting even without sleeping arms, (ii) the lack of theory under adversarially varying availability, and (iii) the consistently weak empirical performance of CTS with Gaussian priors (CTS-G). This paper resolves these long-standing issues by providing the first worst-case regret analysis of CTS-G, proving an upper bound of $\tilde{O}(m\sqrt{NT})$ and a matching lower bound of $\tildeΩ(m\sqrt{NT})$. To bridge the gap between theory and practice, we further propose CL-SG, a simple CTS-G variant that samples a single shared Gaussian seed each round to coordinate exploration across arms. We show that CL-SG achieves an improved regret bound of $\tilde{O}(\sqrt{mNT})$, together with a matching lower bound $Ω(\sqrt{mNT})$. Experiments on real-world datasets demonstrate that CL-SG consistently outperforms strong baselines including CTS-G and CTS-B, and we open-source our implementation for reproducibility.

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preprint2022arXiv

A bijection between $K$-Kohnert diagrams and reverse set-valued tableaux

Lascoux polynomials are $K$-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux ($\mathsf{RSVT}$) rule for Lascoux polynomials and reverse semistandard Young tableaux ($\mathsf{RSSYT}$) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with $\mathsf{RSSYT}$. Ross and Yong introduced $K$-Kohnert diagrams, which are analogues of Kohnert diagrams. They conjectured a $K$-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between $\mathsf{RSVT}$ and $K$-Kohnert diagrams.

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preprint2021arXiv

Random Distances Associated with Hexagons

In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent hexagons sharing a side, respectively. Simulation results show the accuracy of the obtained closed-form distance distribution functions, which are important in a wide variety of applied sciences and engineering fields. In particular, hexagons are often used in wireless communication networks such as the cellular systems. The correctness of these distance distribution functions is validated by a recursion and a probabilistic sum. The first two statistical moments of the random distances, and the polynomial fits of the density functions are also given in this report for practical uses.

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preprint2020arXiv

A crystal on decreasing factorizations in the $0$-Hecke monoid

We introduce a type $A$ crystal structure on decreasing factorizations of fully-commutative elements in the 0-Hecke monoid which we call $\star$-crystal. This crystal is a $K$-theoretic generalization of the crystal on decreasing factorizations in the symmetric group of the first and last author. We prove that under the residue map the $\star$-crystal intertwines with the crystal on set-valued tableaux recently introduced by Monical, Pechenik and Scrimshaw. We also define a new insertion from decreasing factorization to pairs of semistandard Young tableaux and prove several properties, such as its relation to the Hecke insertion and the uncrowding algorithm. The new insertion also intertwines with the crystal operators.

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preprint2020arXiv

Thompson Sampling for Combinatorial Semi-bandits with Sleeping Arms and Long-Term Fairness Constraints

We study the combinatorial sleeping multi-armed semi-bandit problem with long-term fairness constraints~(CSMAB-F). To address the problem, we adopt Thompson Sampling~(TS) to maximize the total rewards and use virtual queue techniques to handle the fairness constraints, and design an algorithm called \emph{TS with beta priors and Bernoulli likelihoods for CSMAB-F~(TSCSF-B)}. Further, we prove TSCSF-B can satisfy the fairness constraints, and the time-averaged regret is upper bounded by $\frac{N}{2η} + O\left(\frac{\sqrt{mNT\ln T}}{T}\right)$, where $N$ is the total number of arms, $m$ is the maximum number of arms that can be pulled simultaneously in each round~(the cardinality constraint) and $η$ is the parameter trading off fairness for rewards. By relaxing the fairness constraints (i.e., let $η\rightarrow \infty$), the bound boils down to the first problem-independent bound of TS algorithms for combinatorial sleeping multi-armed semi-bandit problems. Finally, we perform numerical experiments and use a high-rating movie recommendation application to show the effectiveness and efficiency of the proposed algorithm.

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