8 citations · 13 across the 16 of their papers we have counts for
14 papers · 1 filter
Dot actions and Hessenberg spaces for dihedral groups
Jonathan Boretsky, Reuven Hodges, Nathan Lesnevich +2
Splines on Weyl groups model the equivariant cohomology of regular semisimple Hessenberg varieties, and the natural group action on them encodes the monodromy action. The resulting…
Kleber's conjecture and complementary products of symmetric functions
Reuven Hodges, Hanzhang Yin
We prove Kleber's rectangular-complement conjecture for Schur functions over an arbitrary commutative ring , showing that, for a fixed rectangle, the products , i…
The record statistic and forward stability of Schubert products
Andrew Hardt, Reuven Hodges, Hanzhang Yin
We initiate a probabilistic study of forward stability for products of Schubert polynomials through the record statistic (left-to-right maxima) of permutations. Building on the exp…
Comparability in Bruhat orders
Jonathan Boretsky, Alvaro Cornejo, Reuven Hodges +3
We determine the sharp asymptotic scale of the probability that two uniformly random permutations are comparable in weak Bruhat order, showing that $\mathbb{P}(σ_1 \preceq_W σ_2)=\…
A non-iterative straightening algorithm and orthogonality for skew Schur modules
Reuven Hodges, Hanzhang Yin
We generalize Fulton's determinantal construction of Schur modules to the skew setting, providing an explicit and functorial presentation using only elementary linear algebra and d…
Kohnert posets and polynomials of northeast diagrams
Aram Bingham, Beth Anne Castellano, Kimberly P. Hadaway +4
Kohnert polynomials and their associated posets are combinatorial objects with deep geometric and representation theoretic connections, generalizing both Schubert polynomials and t…
Orbit structures and complexity in Schubert and Richardson Varieties
Yibo Gao, Reuven Hodges
The goal of this paper is twofold. Firstly, we provide a type-uniform formula for the torus complexity of the usual torus action on a Richardson variety, by developing the notion o…
Proper elements of Coxeter groups
József Balogh, David Brewster, Reuven Hodges
We extend the notion of proper elements to all Coxeter groups. For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to z…
Approximate counting of standard set-valued tableaux
Reuven Hodges, Gidon Orelowitz
We present a randomized algorithm for generating standard set-valued tableaux by extending the Green-Nijenhuis-Wilf hook walk algorithm. In the case of asymptotically rank two part…
Classification of Levi-spherical Schubert varieties
Yibo Gao, Reuven Hodges, Alexander Yong
A Schubert variety in the complete flag manifold is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give…
Proper permutations, Schubert geometry, and randomness
David Brewster, Reuven Hodges, Alexander Yong
We define and study proper permutations. Properness is a geometrically natural necessary criterion for a Schubert variety to be Levi-spherical. We prove the probability that a rand…
Multiplicity-free skew Schur polynomials
Shiliang Gao, Reuven Hodges, Gidon Orelowitz
We provide a non-recursive, combinatorial classification of multiplicity-free skew Schur polynomials. These polynomials are , and , characters of the skew Schur modules…
Multiplicity-free key polynomials
Reuven Hodges, Alexander Yong
The key polynomials, defined by A. Lascoux-M.-P. Schützenberger, are characters for the Demazure modules of type A. We classify multiplicity-free key polynomials. The proof uses tw…
A non-iterative formula for straightening fillings of Young diagrams
Reuven Hodges
Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straig…