@article{gunawan_pan_russell_tenner_2024, title={Runs and RSK Tableaux of Boolean Permutations}, volume={4}, ISSN={["0219-3094"]}, DOI={10.1007/s00026-024-00689-z}, journal={ANNALS OF COMBINATORICS}, author={Gunawan, Emily and Pan, Jianping and Russell, Heather M. and Tenner, Bridget Eileen}, year={2024}, month={Apr} }
 @article{pan_yu_2023, title={A Bijection Between <i>K</i>-Kohnert Diagrams and Reverse Set-Valued Tableaux}, volume={30}, ISSN={["1077-8926"]}, url={http://dx.doi.org/10.37236/11434}, DOI={10.37236/11434}, abstractNote={Lascoux polynomials are K-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux (RSVT) rule for Lascoux polynomials and reverse semistandard Young tableaux (RSSYT) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with 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 RSVT and K-Kohnert diagrams.}, number={4}, journal={ELECTRONIC JOURNAL OF COMBINATORICS}, author={Pan, Jianping and Yu, Tianyi}, year={2023}, month={Nov} }
 @article{gunawan_pan_russell_tenner_2023, title={RSK tableaux and the weak order on fully commutative permutations}, volume={30}, ISSN={["1077-8926"]}, DOI={10.37236/11877}, abstractNote={For each fully commutative permutation, we construct a “boolean core,” which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the recently defined crowded and uncrowded elements, distinguished by whether or not their RSK insertion tableaux satisfy a sparsity condition. We show that a fully commutative element is uncrowded exactly when it shares the RSK insertion tableau with its boolean core. We present the dynamics of the right weak order on fully commutative permutations, with particular interest in when they change from uncrowded to crowded. In particular, we use consecutive permutation patterns and descents to characterize the minimal crowded elements under the right weak order.}, number={4}, journal={ELECTRONIC JOURNAL OF COMBINATORICS}, author={Gunawan, Emily and Pan, Jianping and Russell, Heather M. and Tenner, Bridget Eileen}, year={2023}, month={Dec} }
 @book{pan_yu_2023, title={Top-degree components of Grothendieck and Lascoux polynomials}, DOI={10.48550/arXiv.2302.03643}, abstractNote={The Castelnuovo-Mumford polynomial $\widehat{\mathfrak{G}}_w$ with $w \in S_n$ is the highest homogeneous component of the Grothendieck polynomial $\mathfrak{G}_w$. Pechenik, Speyer and Weigandt define a statistic $\mathsf{rajcode}(\cdot)$ on $S_n$ that gives the leading monomial of $\widehat{\mathfrak{G}}_w$. We introduce a statistic $\mathsf{rajcode}(\cdot)$ on any diagram $D$ through a combinatorial construction ``snow diagram'' that augments and decorates $D$. When $D$ is the Rothe diagram of a permutation $w$, $\mathsf{rajcode}(D)$ agrees with the aforementioned $\mathsf{rajcode}(w)$. When $D$ is the key diagram of a weak composition $\alpha$, $\mathsf{rajcode}(D)$ yields the leading monomial of $\widehat{\mathfrak{L}}_\alpha$, the highest homogeneous component of the Lascoux polynomials $\mathfrak{L}_\alpha$. We use $\widehat{\mathfrak{L}}_\alpha$ to construct a basis of $\widehat{V}_n$, the span of $\widehat{\mathfrak{G}}_w$ with $w \in S_n$. Then we show $\widehat{V}_n$ gives a natural algebraic interpretation of a classical $q$-analogue of Bell numbers.}, number={2302.036432302.03643}, author={Pan, J. and Yu, T.}, year={2023} }
 @book{pan_yu_2022, title={A Bijection between K-Kohnert Diagrams and Reverse Set-Valued Tableaux}, DOI={10.48550/arXiv.2206.08993}, abstractNote={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.}, number={2206.089932206.08993}, author={Pan, J. and Yu, T.}, year={2022} }
 @book{gunawan_pan_russell_tenner_2022, title={RSK tableaux and the weak order on fully commutative permutations}, url={arXiv:2212.05002}, DOI={10.48550/arXiv.2212.05002}, abstractNote={For each fully commutative permutation, we construct a "boolean core," which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the recently defined crowded and uncrowded elements, distinguished by whether or not their RSK insertion tableaux satisfy a sparsity condition. We show that a fully commutative element is uncrowded exactly when it shares the RSK insertion tableau with its boolean core. We present the dynamics of the right weak order on fully commutative permutations, with particular interest in when they change from uncrowded to crowded. In particular, we use consecutive permutation patterns and descents to characterize the minimal crowded elements under the right weak order.}, number={2212.050022212.05002}, author={Gunawan, E. and Pan, J. and Russell, H.M. and Tenner, B.E.}, year={2022} }
 @book{gunawan_pan_russell_tenner_2022, title={Runs and RSK tableaux of boolean permutations}, url={https://arxiv.org/abs/2207.05119}, DOI={10.48550/arXiv.2207.05119}, abstractNote={We define and construct the "canonical reduced word" of a boolean permutation, and show that the RSK tableaux for that permutation can be read off directly from this reduced word. We also describe those tableaux that can correspond to boolean permutations, and enumerate them. In addition, we generalize a result of Mazorchuk and Tenner, showing that the "run" statistic influences the shape of the RSK tableau of arbitrary permutations, not just of those that are boolean.}, number={2207.051192207.05119}, institution={arXiv}, author={Gunawan, E. and Pan, J. and Russell, H.M. and Tenner, B.E.}, year={2022} }
 @article{pan_pappe_poh_schilling_2022, title={Uncrowding Algorithm for Hook-Valued Tableaux}, volume={26}, ISSN={0218-0006 0219-3094}, url={http://dx.doi.org/10.1007/s00026-022-00567-6}, DOI={10.1007/s00026-022-00567-6}, abstractNote={Abstract}, number={1}, journal={Annals of Combinatorics}, publisher={Springer Science and Business Media LLC}, author={Pan, Jianping and Pappe, Joseph and Poh, Wencin and Schilling, Anne}, year={2022}, month={Jan}, pages={261–301} }
 @article{morse_pan_poh_schilling_2020, title={A Crystal on Decreasing Factorizations in the 0-Hecke Monoid}, volume={27}, ISSN={1077-8926}, url={http://dx.doi.org/10.37236/9168}, DOI={10.37236/9168}, abstractNote={We introduce a type $A$ crystal structure on decreasing factorizations of fully-commu\-tative 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.}, number={2}, journal={The Electronic Journal of Combinatorics}, publisher={The Electronic Journal of Combinatorics}, author={Morse, Jennifer and Pan, Jianping and Poh, Wencin and Schilling, Anne}, year={2020}, month={May} }
 @inproceedings{morse_pan_poh_schilling_2020, title={Crystal for Stable Grothendieck Polynomials}, booktitle={Proceedings of of the 32nd Conference on Formal Power Series and Algebraic Combinatorics}, author={Morse, J. and Pan, J. and Poh, W. and Schilling, A.}, year={2020} }
 @article{pan_scrimshaw_2017, title={Virtualization Map for the Littelmann Path Model}, volume={23}, ISSN={1083-4362 1531-586X}, url={http://dx.doi.org/10.1007/s00031-017-9456-3}, DOI={10.1007/s00031-017-9456-3}, abstractNote={We show the natural embedding of weight lattices from a diagram folding is a virtualization map for the Littelmann path model, which recovers a result of Kashiwara. As an application, we give a type-independent proof that certain Kirillov-Reshetikhin crystals respect diagram foldings, which is a known result on a special case of a conjecture given by Okado, Schilling, and Shimozono.}, number={4}, journal={Transformation Groups}, publisher={Springer Science and Business Media LLC}, author={Pan, Jianping and Scrimshaw, Travis}, year={2017}, month={Nov}, pages={1045–1061} }