9 papers
Towards combinatorial derivations of K-polynomials for determinantal varieties
Liam Buttitta, Ada Stelzer
Let denote the variety of complex matrices with rank at most . The power series and rational expressions for the Hilbert se…
Plane partitions and spin adapted quantum states
Abigail Price, Ada Stelzer, Svala Sverrisdóttir
We describe an explicit basis for the -invariant space of the exterior power via the combinatorics of plane partitions. In quant…
Gröbner crystal structures
Abigail Price, Ada Stelzer, Alexander Yong
We develop a theory of bicrystalline ideals, synthesizing Gröbner basis techniques and Kashiwara's crystal theory. This provides a unified algebraic, combinatorial, and computation…
Sums of Schubert structure constants with bounded Coxeter length
Ada Stelzer
Pak-Robichaux recently introduced a signed puzzle rule for Schubert structure constants, which they use to show that sums of these constants with a bounded number of inver…
RSK as a linear operator
Ada Stelzer, Alexander Yong
The Robinson-Schensted-Knuth correspondence (RSK) is a bijection between nonnegative integer matrices and pairs of Young tableaux. We study it as a linear operator on the coordinat…
Representations from matrix varieties, and filtered RSK
Abigail Price, Ada Stelzer, Alexander Yong
Matrix Schubert varieties (Fulton '92) carry natural actions of Levi groups. Their coordinate rings are thereby Levi-representations; what is a combinatorial counting rule for the…
Schubert determinantal ideals are Hilbertian
Ada Stelzer, Alexander Yong
Abhyankar defined an ideal to be Hilbertian if its Hilbert polynomial coincides with its Hilbert function for all nonnegative integers. In 1984, he proved that the ideal of (r+1)-o…
Matrix Schubert varieties, binomial ideals, and reduced Gröbner bases
Ada Stelzer
We prove a sharp lower bound on the number of terms in an element of the reduced Gröbner basis of a Schubert determinantal ideal under the term order of [Knutson-Miller '05].…
Combinatorial commutative algebra rules
Ada Stelzer, Alexander Yong
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study…