37 citations · 313 across the 41 of their papers we have counts for
5 papers · 1 filter
Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley
Zachary Hamaker, Oliver Pechenik, David E Speyer +1
We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a de…
The genomic Schur function is fundamental-positive
Oliver Pechenik
In work with A. Yong, the author introduced genomic tableaux to prove the first positive combinatorial rule for the Littlewood-Richardson coefficients in torus-equivariant -theo…
Crystal structures for symmetric Grothendieck polynomials
Cara Monical, Oliver Pechenik, Travis Scrimshaw
The symmetric Grothendieck polynomials representing Schubert classes in the -theory of Grassmannians are generating functions for semistandard set-valued tableaux. We construct…
Polynomials from combinatorial -theory
Cara Monical, Oliver Pechenik, Dominic Searles
We introduce two new bases of the ring of polynomials and study their relations to known bases. The first basis is the quasiLascoux basis, which is simultaneously both a -theore…
Unique rectification in -complete posets: towards the -theory of Kac-Moody flag varieties
Rahul Ilango, Oliver Pechenik, Michael Zlatin
The jeu-de-taquin-based Littlewood-Richardson rule of H. Thomas and A. Yong (2009) for minuscule varieties has been extended in two orthogonal directions, either enriching the coho…