Search Results - "Speyer, David"
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1
Weak separation and plabic graphs
Published in Proceedings of the London Mathematical Society (01-03-2015)“…Leclerc and Zelevinsky described quasicommuting families of quantum minors in terms of a certain combinatorial condition, called weak separation. They…”
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Cohomology of cluster varieties II: Acyclic case
Published in Journal of the London Mathematical Society (01-12-2023)“…In the previous work, we initiated the study of the cohomology of locally acyclic cluster varieties. In the present work, we show that the mixed Hodge…”
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3
The fundamental theorem of finite semidistributive lattices
Published in Selecta mathematica (Basel, Switzerland) (01-09-2021)“…We prove a Fundamental Theorem of Finite Semidistributive Lattices (FTFSDL), modelled on Birkhoff’s Fundamental Theorem of Finite Distributive Lattices. Our…”
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Cluster algebras of Grassmannians are locally acyclic
Published in Proceedings of the American Mathematical Society (01-08-2016)“…Considered as commutative algebras, cluster algebras can be very unpleasant objects. However, the first author introduced a condition known as ``local…”
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5
Castelnuovo–Mumford regularity of matrix Schubert varieties
Published in Selecta mathematica (Basel, Switzerland) (01-09-2024)“…Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete flag variety. We give a formula for the Castelnuovo–Mumford…”
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The positive Dressian equals the positive tropical Grassmannian
Published in Transactions of the American Mathematical Society. Series B (09-04-2021)“…The Dressian and the tropical Grassmannian parameterize abstract and realizable tropical linear spaces; but in general, the Dressian is much larger than the…”
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7
Powers of Coxeter Elements in Infinite Groups Are Reduced
Published in Proceedings of the American Mathematical Society (01-04-2009)“…Let W be an infinite irreducible Coxeter group with (s₁,..., $s_{n}$) the simple generators. We give a short proof that the word $s_{1}s_{2}\cdots…”
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K -classes for matroids and equivariant localization
Published in Duke mathematical journal (01-11-2012)“…To every matroid, we associate a class in the K -theory of the Grassmannian. We study this class by using the method of equivariant localization. In…”
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Variations on a theme of Kasteleyn, with Application to the Totally Nonnegative Grassmannian
Published in The Electronic journal of combinatorics (29-04-2016)“…We provide a short proof of a classical result of Kasteleyn, and prove several variants thereof. One of these results has become key in the parametrization of…”
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10
Sortable elements in infinite Coxeter groups
Published in Transactions of the American Mathematical Society (01-02-2011)“…In a series of previous papers, we studied sortable elements in finite Coxeter groups, and the related Cambrian fans. We applied sortable elements and Cambrian…”
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The growth rate of tri-colored sum-free sets
Published in Discrete analysis (06-07-2018)“…The growth rate of tri-colored sum-free sets, Discrete Analysis 2018:12, 10 pp. This paper contributes to the remarkable collection of results that followed in…”
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12
A Counting Proof of a Theorem of Frobenius
Published in The American mathematical monthly (01-04-2017)“…Frobenius showed that, if m divides the order of a finite group, then the number of m-torsion elements in that group is divisible by m. We provide a quick…”
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13
Links in the complex of weakly separated collections
Published in Discrete Mathematics and Theoretical Computer Science (22-04-2020)“…Plabic graphs are combinatorial objects used to study the totally nonnegative Grassmannian. Faces of plabic graphs are labeled by k-element sets of positive…”
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Journal Article Conference Proceeding -
14
Schubert problems with respect to osculating flags of stable rational curves
Published in Algebraic geometry (01-01-2014)Get full text
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Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley
Published in Algebraic combinatorics (2020)Get full text
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Cambrian frameworks for cluster algebras of affine type
Published in Transactions of the American Mathematical Society (01-02-2018)“…We give a combinatorial model for the exchange graph and \mathbf {g}-vector fan associated to any acyclic exchange matrix B of affine type. More specifically,…”
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A Cambrian Framework for the Oriented Cycle
Published in The Electronic journal of combinatorics (23-12-2015)“…This paper completes the project of constructing combinatorial models (called frameworks) for the exchange graph and $\mathbf{g}$-vector fan associated to any…”
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Perfect matchings and the octahedron recurrence
Published in Journal of algebraic combinatorics (01-05-2007)Get full text
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The twist for positroids
Published in Discrete Mathematics and Theoretical Computer Science (22-04-2020)“…There are two reasonable ways to put a cluster structure on a positroid variety. In one, the initial seed is a set of Plu ̈cker coordinates. In the other, the…”
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Journal Article Conference Proceeding -
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The twist for positroid varieties
Published in Proceedings of the London Mathematical Society (01-11-2017)“…The purpose of this document is to connect two maps related to certain graphs embedded in the disc. The first is Postnikov's boundary measurement map, which…”
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