Publications (20)
Grothendieck positivity for normal square root crystals
Eric Marberg, Kam Hung Tong, Tianyi Yu
Normal crystals (also known as Stembridge crystals) are commonly used to establish the Schur positivity of symmetric functions, as their characters are sums of Schur polynomials. I…
Listwise Direct Preference Optimization with Multi-Dimensional Preference Mixing
Yuhui Sun, Xiyao Wang, Zixi Li +6
Recent alignment methods based on Direct Preference Optimization (DPO) reformulate preference learning as supervised optimization over pairwise comparisons, offering improved effic…
Grothendieck polynomials of inverse fireworks permutations
Chen-An Chou, Tianyi Yu
Pipedreams are combinatorial objects that compute Grothendieck polynomials. We introduce a new combinatorial object that naturally recast the pipedream formula. From this, we obtai…
A positive combinatorial formula for the double Edelman--Greene coefficients
Jack Chen-An Chou, Tianyi Yu
Lam, Lee, and Shimozono introduced the double Stanley symmetric functions in their study of the equivariant geometry of the affine Grassmannian. They proved that the associated dou…
Tableau formula for vexillary double Edelman--Greene coefficients
Adam Gregory, Zachary Hamaker, Tianyi Yu
Lam, Lee and Shimozono recently introduced backstable double Grothendieck polynomials to represent -theory classes of the infinite flag variety. They used them to define double…
Grothendieck to Lascoux expansions
Mark Shimozono, Tianyi Yu
We establish the conjecture of Reiner and Yong for an explicit combinatorial formula for the expansion of a Grothendieck polynomial into the basis of Lascoux polynomials. This expa…
A Creativity Survey of Parallel Sorting Algorithm
Tianyi Yu, Wei Li
Sorting is one of the most fundamental problems in the field of computer science. With the rapid development of manycore processors, it shows great importance to design efficient p…
Lascoux expansion of the product of a Lascoux and a stable Grothendieck
Gidon Orelowitz, Tianyi Yu
This paper gives a tableau formula for expanding the product of a Lascoux polynomial and a stable Grothendieck polynomial into Lascoux polynomials. Lascoux and stable Grothendieck…
Top-degree components of Grothendieck and Lascoux polynomials
Jianping Pan, Tianyi Yu
The Castelnuovo-Mumford polynomial with is the highest homogeneous component of the Grothendieck polynomial . Pechenik, Speye…
Harmonic bases for generalized coinvariant algebras
Brendon Rhoades, Tianyi Yu, Zehong Zhao
Let be nonnegative integers and let be a partition of . S. Griffin recently introduced a quotient of the polynomial ring …
Constructing maximal pipedreams of double Grothendieck polynomials
Chen-An Chou, Tianyi Yu
Pechenik, Speyer and Weigandt defined a statistic on permutations which characterizes the leading monomial in top degree components of double Grothendieck…
A bijection between -Kohnert diagrams and reverse set-valued tableaux
Jianping Pan, Tianyi Yu
Lascoux polynomials are -theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux () rule…
Embedding bumpless pipedreams as Bruhat chains
Tianyi Yu
Schubert polynomials are distinguished representatives of Schubert cycles in the cohomology of the flag variety. In the spirit of Bergeron and Sottile, we use the Bruhat order to g…
Connection between Schubert polynomials and top Lascoux polynomials
Tianyi Yu
Schubert polynomials form a basis of the polynomial ring. This basis and its structure constants have received extensive study. Recently, Pan and Yu initiated the study of top Lasc…
Constructing a Gröbner basis of Griffin's ideal
Tianyi Yu
In his Ph.D. thesis, Sean Griffin introduced a family of ideals and found monomial bases for their quotient rings. These rings simultaneously generalize the Delta Conjecture coinva…
Federated Graph-based Networks with Shared Embedding
Tianyi Yu, Pei Lai, Fei Teng
Nowadays, user privacy is becoming an issue that cannot be bypassed for system developers, especially for that of web applications where data can be easily transferred through inte…
Marked Bumpless Pipedreams and Compatible Pairs
Daoji Huang, Mark Shimozono, Tianyi Yu
We construct a bijection between marked bumpless pipedreams with reverse compatible pairs, which are in bijection with not-necessarily-reduced pipedreams. This directly unifies var…
Set-valued tableaux rule for Lascoux polynomials
Tianyi Yu
Lascoux polynomials generalize Grassmannian stable Grothendieck polynomials and may be viewed as K-theoretic analogs of key polynomials. The latter two polynomials have combinatori…
A row analogue of Hecke column insertion
Daoji Huang, Mark Shimozono, Tianyi Yu
We introduce a new row insertion algorithm on decreasing tableaux and increasing tableaux, generalizing Edelman-Greene (EG) row insertion. Our row insertion algorithm is a nontrivi…
MirrorCraft: Paired Evaluation under Hidden Rule Changes in Minecraft
Jianxin Gao, Beini Hu, Runze Li +6
With the prosperity of the large language models (LLMs), it has become an interesting topic: how do LLM-based agents work in Minecraft? Unfortunately, most existing benchmarks eval…