37 citations · 313 across the 41 of their papers we have counts for
41 papers
Mixed jeu de taquin and a problem of Soojin Cho
Santiago Estupiñán-Salamanca, Oliver Pechenik
Serrano (2010) introduced the shifted plactic monoid, governing Haiman's (1989) mixed insertion algorithm, as a type B analogue of the classical plactic monoid that connects jeu de…
Promotion digraphs
Rebecca Patrias, Oliver Pechenik, Jessica Striker
Work of Gaetz, Pechenik, Pfannerer, Striker, and Swanson (2024) introduced promotion permutations for a rectangular standard Young tableau . These promotion permutations encode…
Degrees of P-Grothendieck polynomials and regularity of Pfaffian varieties
Oliver Pechenik, Matthew St. Denis
We prove a formula for the degrees of Ikeda and Naruse's -Grothendieck polynomials using combinatorics of shifted tableaux. We show this formula can be used in conjunction with…
Web bases in degree two from hourglass plabic graphs
Christian Gaetz, Oliver Pechenik, Stephan Pfannerer +2
Webs give a diagrammatic calculus for spaces of -tensor invariants, but intrinsic characterizations of web bases are only known in certain cases. Recently, we…
Web invariants for flamingo Specht modules
Chris Fraser, Rebecca Patrias, Oliver Pechenik +1
Webs yield an especially important realization of certain Specht modules, irreducible representations of symmetric groups, as they provide a pictorial basis with a convenient diagr…
Promotion permutations for tableaux
Christian Gaetz, Oliver Pechenik, Stephan Pfannerer +2
In our companion paper, we develop a new -web basis. Basis elements are given by certain planar graphs and are constructed so that important algebraic operations can be perfo…
Rotation-invariant web bases from hourglass plabic graphs
Christian Gaetz, Oliver Pechenik, Stephan Pfannerer +2
Webs give a diagrammatic calculus for spaces of tensor invariants. We introduce hourglass plabic graphs as a new avatar of webs, and use these to give the first rotation-invariant…
James reduced product schemes and double quasisymmetric functions
Oliver Pechenik, Matthew Satriano
Symmetric function theory is a key ingredient in the Schubert calculus of Grassmannians. Quasisymmetric functions are analogues that are similarly central to algebraic combinatoric…
The Kromatic Symmetric Function: A -theoretic Analogue of
Logan Crew, Oliver Pechenik, Sophie Spirkl
Schur functions are a basis of the symmetric function ring that represent Schubert cohomology classes for Grassmannians. Replacing the cohomology ring with -theory yields a rich…
Quasisymmetric Schubert calculus
Oliver Pechenik, Matthew Satriano
The ring of symmetric functions occupies a central place in algebraic combinatorics, with a particularly notable role in Schubert calculus, where the standard cell decompositions o…
Proof of a conjectured Möbius inversion formula for Grothendieck polynomials
Oliver Pechenik, Matthew Satriano
Schubert polynomials are polynomial representatives for cohomology classes of Schubert varieties in a complete flag variety, while Grothendieck polynomials $\mathf…
An inverse Grassmannian Littlewood-Richardson rule and extensions
Oliver Pechenik, Anna Weigandt
Chow rings of flag varieties have bases of Schubert cycles , indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula fo…
Curious cyclic sieving on increasing tableaux
Christian Gaetz, Oliver Pechenik, Jessica Striker +1
We prove a cyclic sieving result for the set of packed increasing tableaux with maximum entry under K-promotion. The "curiosity" is that the sieving polynomi…
A web basis of invariant polynomials from noncrossing partitions
Rebecca Patrias, Oliver Pechenik, Jessica Striker
The irreducible representations of symmetric groups can be realized as certain graded pieces of invariant rings, equivalently as global sections of line bundles on partial flag var…
Castelnuovo-Mumford regularity of matrix Schubert varieties
Oliver Pechenik, David E Speyer, Anna Weigandt
Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete flag variety. We give a formula for the Castelnuovo-Mumford regularity of matrix Sch…
Tableau evacuation and webs
Rebecca Patrias, Oliver Pechenik
Webs are certain planar diagrams embedded in disks. They index and describe bases of tensor products of representations of and . There are explic…
Minuscule analogues of the plane partition periodicity conjecture of Cameron and Fon-Der-Flaass
Oliver Pechenik
Let be a graded poset of rank and let be a -element chain. For an order ideal of , its rowmotion is the smallest ideal conta…
Path-cordial abelian groups
Rebecca Patrias, Oliver Pechenik
A labeling of the vertices of a graph by elements of any abelian group induces a labeling of the edges by summing the labels of their endpoints. Hovey defined the graph to…
Gröbner geometry of Schubert polynomials through ice
Zachary Hamaker, Oliver Pechenik, Anna Weigandt
The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson and Miller (2005) via antidiagonal Gröbner degenerati…
Dynamics of plane partitions: Proof of the Cameron-Fon-Der-Flaass conjecture
Rebecca Patrias, Oliver Pechenik
One of the oldest outstanding problems in dynamical algebraic combinatorics is the following conjecture of P. Cameron and D. Fon-Der-Flaass (1995). Consider a plane partition i…
Asymmetric function theory
Oliver Pechenik, Dominic Searles
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. M…
K-theoretic crystals for set-valued tableaux of rectangular shapes
Oliver Pechenik, Travis Scrimshaw
In earlier work with C.~Monical, we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured th…
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…