Works (53)
Updated: April 4th, 2024 13:54
2022 article
DOMINANCE PHENOMENA: MUTATION, SCATTERING AND CLUSTER ALGEBRAS
Reading, N. (2022, October 28). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol. 10.
arxiv.org (repository)
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: November 21, 2022
2021 journal article
The fundamental theorem of finite semidistributive lattices
SELECTA MATHEMATICA-NEW SERIES, 27(4).
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: September 13, 2021
2020 journal article
An affine almost positive roots model
Journal of Combinatorial Algebra.
author keywords: Almost-positive roots; compatibility degree; cluster algebras; denominator vectors; g-vectors; affine root systems; affine generalized associahedra; exchangeable roots
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Source: ORCID
Added: April 28, 2020
2020 journal article
Scattering Fans
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2020(23), 9640–9673.
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: January 25, 2021
2020 journal article
The action of a Coxeter element on an affine root system
Proceedings of the American Mathematical Society.
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Source: ORCID
Added: April 28, 2020
2019 journal article
Lattice homomorphisms between weak orders
Electron. J. Combin., 26(2), Paper 2.23, 50. http://www.scopus.com/inward/record.url?eid=2-s2.0-85067350483&partnerID=MN8TOARS
Source: ORCID
Added: December 4, 2019
2018 journal article
Coxeter-biCatalan combinatorics
JOURNAL OF ALGEBRAIC COMBINATORICS, 47(2), 241–300.
author keywords: Alternating arc diagram; Coxeter-Catalan combinatorics; Doubled root poset; Twin clusters; Twin noncrossing partitions; Twin nonnesting partitions; Twin sortable elements
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2018 journal article
INITIAL-SEED RECURSIONS AND DUALITIES FOR d-VECTORS
PACIFIC JOURNAL OF MATHEMATICS, 293(1), 179–206.
author keywords: cluster algebra; denominator vector; initial-seed recursion; marked surface
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2018 journal article
Lattice structure of Weyl groups via representation theory of preprojective algebras
COMPOSITIO MATHEMATICA, 154(6), 1269–1305.
Contributors: O. Iyama, * , I. Reiten & H. Thomas *
author keywords: preprojective algebra; Weyl group; weak order; tau-tilting theory; brick; join-irreducible element; lattice congruence
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2018 journal article
Universal Geometric Coefficients for the Four-Punctured Sphere
Annals of Combinatorics, 22(1), 1–44.
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2017 journal article
Cambrian frameworks for cluster algebras of affine type
Transactions of the American Mathematical Society, 370(2), 1429–1468.
UN Sustainable Development Goal Categories
4. Quality Education
(OpenAlex)
15. Life on Land
(Web of Science)
Sources: ORCID, Crossref, NC State University Libraries
Added: June 30, 2019
2016 journal article
Combinatorial Frameworks for Cluster Algebras
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016(1), 109–173.
TL;DR:
This paper uses sortable elements to construct a framework for any cluster algebra with an acyclic initial exchange matrix to produce a complete framework for a cluster algebra whose associated Cartan matrix is of affine type.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2016 journal article
Coxeter arrangements in three dimensions
Beiträge Zur Algebra Und Geometrie / Contributions to Algebra and Geometry, 57(4), 891–897.
Contributors: R. Ehrenborg *, C. Klivans* & n
author keywords: Hyperplane arrangements; Finite Coxeter systems; Spherical geometry
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2016 chapter
Finite Coxeter Groups and the Weak Order
In Lattice Theory: Special Topics and Applications (Vol. 2, pp. 489–561).
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2016 chapter
Lattice Theory of the Poset of Regions
In Lattice Theory: Special Topics and Applications (Vol. 2, pp. 399–487).
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2015 journal article
A Cambrian framework for the oriented cycle
Electron. J. Combin., 22(4), Paper 4.46, 21. http://www.scopus.com/inward/record.url?eid=2-s2.0-84951847857&partnerID=MN8TOARS
Sources: NC State University Libraries, ORCID
Added: August 6, 2018
2015 journal article
Coxeter-biCatalan combinatorics
Discrete Mathematics & Theoretical Computer Science.
Source: ORCID
Added: January 9, 2023
2015 journal article
NONCROSSING ARC DIAGRAMS AND CANONICAL JOIN REPRESENTATIONS
SIAM JOURNAL ON DISCRETE MATHEMATICS, 29(2), 736–750.
author keywords: canonical join representation; lattice congruence; noncrossing arc diagram; permutation; weak order
TL;DR:
This work considers two problems that appear at first sight to be unrelated, but turn out to be closely related because the noncrossing arc diagrams provide a combinatorial model for canonical join representations.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
Universal geometric coefficients for the once-punctured torus
Séminaire Lotharingien De Combinatoire, B71e, Art. B71e, 29. http://math.univ-lyon1.fr/~slc/wpapers/s71reading.html
Sources: NC State University Libraries, ORCID
Added: July 28, 2019
2014 journal article
UNIVERSAL GEOMETRIC CLUSTER ALGEBRAS FROM SURFACES
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 366(12), 6647–6685.
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2014 journal article
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2012 journal article
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018
2012 chapter
From the Tamari lattice to Cambrian lattices and beyond
In F. Mueller-Hoissen, J. Pallo, & J. Stasheff (Eds.), Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift (pp. 293–322).
Ed(s): F. Mueller-Hoissen, J. Pallo & J. Stasheff
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: December 4, 2019
2012 journal article
TL;DR:
The enumeration of generic rectangulations up to combinatorial equivalence is initiated by establishing an explicit bijection between generic rectagulations and a set of permutations defined by a pattern-avoidance condition analogous to the definition of the twisted Baxter permutations.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2012 journal article
The Hopf algebra of diagonal rectangulations
JOURNAL OF COMBINATORIAL THEORY SERIES A, 119(3), 788–824.
Contributors: S. Law n & n
author keywords: Baxter permutation; Diagonal rectangulation; Hopf algebra
TL;DR:
A combinatorial Hopf algebra dRec with basis elements indexed by diagonal rectangulations of a square is defined and an explicit bijection between twisted Baxter permutations and the better-known Baxter permutation is given, and the resulting Hopfgebra structure on Baxter perm mutations is described.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2011 journal article
Noncrossing partitions and the shard intersection order
JOURNAL OF ALGEBRAIC COMBINATORICS, 33(4), 483–530.
author keywords: Noncrossing partition; Shard; Coxeter group; Weak order
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2011 journal article
SORTABLE ELEMENTS IN INFINITE COXETER GROUPS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(2), 699–761.
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2010 journal article
Noncrossing partitions, clusters and the Coxeter plane
Séminaire Lotharingien De Combinatoire, 63, B63b. https://www.mat.univie.ac.at/~slc/wpapers/s63reading.html
Sources: ORCID, NC State University Libraries
Added: December 4, 2019
2010 journal article
Sortable elements for quivers with cycles
The Electronic Journal of Combinatorics, 17(1), R90.
TL;DR:
This paper defines a more general notion of $\Omega$-sortable elements, where $\ Omega$ is an arbitrary orientation of the Coxeter diagram, and shows that the key properties of $c$- Sortable elements carry over to the $\O Omega$- sortable elements.
(via Semantic Scholar)
Sources: NC State University Libraries, ORCID
Added: December 4, 2019
2010 journal article
Sortable elements for quivers with cycles
Electronic Journal of Combinatorics, 17(1), 1–19. http://www.scopus.com/inward/record.url?eid=2-s2.0-77955640004&partnerID=MN8TOARS
Source: ORCID
Added: January 16, 2020
2009 journal article
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018
2009 journal article
Noncrossing partitions and the shard intersection order
Discrete Mathematics & Theoretical Computer Science.
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(OpenAlex)
Source: ORCID
Added: February 1, 2024
2009 conference paper
Noncrossing partitions and the shard intersection order
FPSAC'09 - 21st International Conference on Formal Power Series and Algebraic Combinatorics, 745–756. http://www.scopus.com/inward/record.url?eid=2-s2.0-79954628162&partnerID=MN8TOARS
Source: ORCID
Added: January 16, 2020
2008 journal article
Chains in the noncrossing partition lattice
SIAM JOURNAL ON DISCRETE MATHEMATICS, 22(3), 875–886.
author keywords: absolute order; Catalan number; chain enumeration; Coxeter element; Coxeter group; generalized cluster complex; noncrossing partition; parking function
TL;DR:
A simpler proof of a known uniform formula for the number of maximal chains of noncrossing partitions and a new uniform formula that is proven uniformly in a general relation is obtained.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2007 journal article
Clusters, coxeter-sortable elements and noncrossing partitions
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 359(12), 5931–5958.
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2007 conference paper
Clusters, noncrossing partitions and the Coxeter plane
FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics. http://www.scopus.com/inward/record.url?eid=2-s2.0-84860725128&partnerID=MN8TOARS
Source: ORCID
Added: January 16, 2020
2007 chapter
Root systems and generalized associahedra
In Geometric Combinatorics (Vol. 13, pp. 63–131).
Sources: Crossref, ORCID
Added: July 1, 2019
2007 journal article
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2006 journal article
author keywords: cluster; Coxeter group; fiber polytope; generalized associahedron; lattice congruence; lattice quotient; Tamari lattice
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2006 conference paper
Clusters, Coxeter-sortable elements and noncrossing partitions
FPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, 275–281. http://www.scopus.com/inward/record.url?eid=2-s2.0-84860648750&partnerID=MN8TOARS
Source: ORCID
Added: January 16, 2020
2005 journal article
Generalized cluster complexes and Coxeter combinatorics
International Mathematics Research Notices, 2005(44), 2709–2757.
Sources: ORCID, NC State University Libraries, NC State University Libraries
Added: December 4, 2019
2005 journal article
Lattice congruences, fans and Hopf algebras
Journal of Combinatorial Theory, Series A, 110(2), 237–273.
author keywords: Coexter group; fan poset; hyperplane arrangement; Malvenuto-Reutenauer Hopf algebra; pattern avoidance; permutohedron; poset of regions; weak order
TL;DR:
It is shown that if a family of lattice congruences On the symmetric groups satisfies certain compatibility conditions then the family defines a sub Hopf algebra of the Malvenuto-Reutenauer Hopfgebra of permutations, which is described by a type of pattern avoidance.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2005 journal article
The order dimension of Bruhat order on infinite Coxeter groups
The Electronic Journal of Combinatorics, 11(2), Research Paper 13, 26. http://www.combinatorics.org/Volume_11/Abstracts/v11i2r13.html
Sources: NC State University Libraries, ORCID
Added: July 10, 2019
2004 journal article
author keywords: Cambrian lattice; congruence uniform; Coxeter group; parabolic subgroup; poset of regions; shard; simplicial hyperplane arrangement; Tamari lattice; weak order
TL;DR:
An algorithm for determining the congruence lattice of the weak order for any finite Coxeter group and for a finite Coxeters group of type A or B is given and a directed graph on subsets or signed subsets is defined such that the transitive closure of the directed graph is the poset of join-irreducibles of the consequences of the strong order.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2004 journal article
Non-negative cd-coefficients of Gorenstein∗ posets
Discrete Mathematics, 274(1-3), 323–329.
author keywords: cd-index; Charney-Davis conjecture; eulerian poset; flag f-vector; Gorenstein
TL;DR:
It is verified, up to rank 6, Stanley's conjecture that the coefficients in the cd-index of a Gorenstein^* ranked poset are non-negative.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2004 journal article
The cd-index of Bruhat intervals
The Electronic Journal of Combinatorics, 11(1), R74.
TL;DR:
A structural recursion on intervals in the Bruhat order gives the isomorphism type of a Bruhat interval in terms of smaller intervals, using basic geometric operations which preserve PL sphericity and have a simple effect on the cd-index, which leads to a new proof that Bruhat intervals are PL spheres.
(via Semantic Scholar)
Sources: NC State University Libraries, ORCID
Added: December 4, 2019
2004 journal article
The cd-index of Bruhat intervals
Electronic Journal of Combinatorics, 11(1 R), 1–25. http://www.scopus.com/inward/record.url?eid=2-s2.0-8744221555&partnerID=MN8TOARS
Source: ORCID
Added: January 16, 2020
2003 journal article
Lattice and order properties of the poset of regions in a hyperplane arrangement
Algebra Universalis, 50(2), 179–205.
author keywords: bounded lattice; Cayley lattice; congruence normal; congruence uniform; Coxeter group; critical pair; doubling; hyperplane arrangement; order dimension; order quotient; permutation lattice; poset of regions; semi-distributive lattice; simplicial; subcritical pair; supersolvable; weak order
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2003 journal article
The order dimension of the poset of regions in a hyperplane arrangement
Journal of Combinatorial Theory, Series A, 104(2), 265–285.
TL;DR:
It is shown that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter Group, and bounds on the order dimensions for the other finite types are given.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 1, 2019
2002 thesis
On the structure of Bruhat order
(ProQuest LLC, Ann Arbor, MI; p. 82). http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3041950
Source: ORCID
Added: December 4, 2019
2002 journal article
Order Dimension, Strong Bruhat Order and Lattice Properties for Posets
Order, 19(1), 73–100.
author keywords: Bruhat; clivage; congruence; Coxeter; critical complex; Dilworth; dissective; distributive lattice; MacNeille completion; monotone triangle; order dimension
TL;DR:
The dissective property is related, via MacNeille completion, to the distributive property of lattices and a similar connection between quotients of the strong Bruhat order with respect to parabolic subgroups and lattice quotients is shown.
(via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: December 4, 2019
1999 journal article
Nim-Regularity of Graphs
The Electronic Journal of Combinatorics, 6(1), Research Paper 11, 8. http://www.combinatorics.org/Volume_6/Abstracts/v6i1r11.html
Sources: NC State University Libraries, ORCID
Added: July 10, 2019
1992 journal article
The thermodynamics of home-made ice cream
Journal of Chemical Education, 69(8), 658–661. http://www.scopus.com/inward/record.url?eid=2-s2.0-27744592214&partnerID=MN8TOARS
Source: ORCID
Added: January 16, 2020
Employment
Updated: January 6th, 2020 11:03
2018 - present
North Carolina State University Raleigh, NC, US
Professor
Mathematics
2012 - 2018
North Carolina State University Raleigh, NC, US
Associate Professor
Mathematics
2006 - 2012
North Carolina State University Raleigh, NC, US
Assistant Professor
Mathematics
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