论文标题
Vexillary grothendieck多项式通过浮力的管道梦
Vexillary Grothendieck Polynomials via Bumpless Pipe Dreams
论文作者
论文摘要
Pechenik，Speyer和Weigandt的最新工作证明了任何Grothendieck多项式程度的公式。 Rajchgot，Robichaux和Weigandt证明了Vexillary Grothendieck多项式程度的独特公式。在这种情况下，我们在特殊情况下提供了Pechenik，Speyer和Weigandt的公式的新证明，并表征了一系列易于度过的Pipe Dreams，这些梦想在这种情况下对Grothendieck多项式贡献了最大程度的术语。此外，我们使用这种表征来在Pechenik-Speyer-Weigandt和Rajchgot-Robichaux-weigandt公式之间建立连接。我们还使用浮力的梦想来证明有关Vexillary Grothendieck多项式支持的新结果，以解决Mészáros，Setiabrata和St. Dizier的猜想的特殊案例。
Recent work of Pechenik, Speyer, and Weigandt proved a formula for the degree of any Grothendieck polynomial. A distinct formula for the degree of vexillary Grothendieck polynomials was proven by Rajchgot, Robichaux, and Weigandt. We give a new proof of Pechenik, Speyer, and Weigandt's formula in the special case of vexillary permutations and characterize the set of bumpless pipe dreams which contribute maximal degree terms to the Grothendieck polynomial in this case. Furthermore, we use this characterization to draw connections between the Pechenik-Speyer-Weigandt and Rajchgot-Robichaux-Weigandt formulas. We also use bumpless pipe dreams to prove new results about the support of vexillary Grothendieck polynomials, addressing special cases of conjectures of Mészáros, Setiabrata, and St. Dizier.
