Tianyi Yu 喻天奕

We show that the generating functions of normal square root crystals are positive sums of symmetric Grothendieck polynomials, providing a tool for establishing Grothendieck positivity.

We give a tableau formula for vexillary double Edelman-Greene coefficients that is manifestly Graham-positive.

Marked bumpless pipedreams and compatible pairs are two combinatorial models for Grothendieck polynomials. We construct a bijection between them.

We reinterpret bumpless pipedreams as Bruhat chains, paralleling Lenart and Sottile’s work on classical pipedreams. This yields a bumpless analogue of Fomin and Stanley’s algebraic construction.

We investigate Grothendieck polynomials labeled by inverse fireworks permutations. We introduce a combinatorial model for their top degree components and proved a conjecture on their support.

We give a tableau formula for the Lascoux expansion of a Lascoux polynomial times a stable Grothendieck polynomial.

We solve a problem of Pechenik, Speyer, and Weigandt on constructing the maximal pipedream that captures the leading monomial of the top-degree part of double Grothendieck polynomials.

We construct an explicit Gröbner basis, with integer coefficients, for a family of ideals introduced by Sean Griffin that generalize the Delta Conjecture coinvariant rings and Springer fiber cohomology rings.

We relate Schubert polynomials and top Lascoux polynomials via a simple operator, showing they share structure constants. This connection uncovers several combinatorial properties of top Lascoux polynomials.

We define a statistic on diagrams. It recovers the rajcode of Pechenik, Speyer, and Weigandt on Rothe diagrams and gives the leading monomial of top Lascoux polynomials on left-justified diagrams.

We introduce a row insertion algorithm on decreasing tableaux that generalizes Edelman–Greene row insertion, serving as a row analogue of Hecke column insertion.

We prove a conjectural formula for Lascoux polynomials by Ross and Yong via a weight-preserving bijection between reverse set-valued tableaux and K-Kohnert diagrams.

We introduce a set-valued tableaux rule for Lascoux polynomials. We construct a new abstract Kashiwara crystal structure on set-valued tableaux.

We prove a conjecture of Reiner and Yong: giving a tableau formula for expanding a Grothendieck polynomial into Lascoux polynomials—analogous to the Schubert-to-key expansion.

We describe the harmonic space and construct a harmonic basis for a family of ideals introduced by Sean Griffin that generalizes the Delta Conjecture coinvariant rings and Springer fiber cohomology rings.