From the 1 of 7 linked papers with an AI index.
7 papers
Kleber's conjecture and complementary products of symmetric functions
Reuven Hodges, Hanzhang Yin
The paper proves Kleber's rectangular‑complement conjecture by showing that products of Schur functions indexed by complementary partition pairs are linearly independent over any c…
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…
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}(Ï_1 \preceq_W Ï_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…
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…