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.

By: N. Reading n

Sources: Web Of Science, ORCID
Added: November 21, 2022

2021 journal article

The fundamental theorem of finite semidistributive lattices

SELECTA MATHEMATICA-NEW SERIES, 27(4).

By: N. Reading n, D. Speyer* & H. Thomas*

co-author countries: Canada 🇨🇦
Sources: Web Of Science, ORCID
Added: September 13, 2021

2020 journal article

An affine almost positive roots model

Journal of Combinatorial Algebra.

Nathan Reading

author keywords: Almost-positive roots; compatibility degree; cluster algebras; denominator vectors; g-vectors; affine root systems; affine generalized associahedra; exchangeable roots
Source: ORCID
Added: April 28, 2020

2020 journal article

Scattering Fans

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2020(23), 9640–9673.

By: N. Reading n

Sources: Web Of Science, ORCID
Added: January 25, 2021

2020 journal article

The action of a Coxeter element on an affine root system

Proceedings of the American Mathematical Society.

Nathan Reading

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

By: N. Reading

Contributors: N. Reading

Source: ORCID
Added: December 4, 2019

2018 journal article

Coxeter-biCatalan combinatorics

JOURNAL OF ALGEBRAIC COMBINATORICS, 47(2), 241–300.

By: E. Barnard n & N. Reading n

Contributors: E. Barnard n & N. Reading n

author keywords: Alternating arc diagram; Coxeter-Catalan combinatorics; Doubled root poset; Twin clusters; Twin noncrossing partitions; Twin nonnesting partitions; Twin sortable elements
Sources: Web Of Science, ORCID
Added: August 6, 2018

2018 journal article

INITIAL-SEED RECURSIONS AND DUALITIES FOR d-VECTORS

PACIFIC JOURNAL OF MATHEMATICS, 293(1), 179–206.

By: N. Reading n & S. Stella*

co-author countries: Israel 🇮🇱

Contributors: N. Reading n & S. Stella*

author keywords: cluster algebra; denominator vector; initial-seed recursion; marked surface
Sources: Web Of Science, ORCID
Added: August 6, 2018

2018 journal article

Lattice structure of Weyl groups via representation theory of preprojective algebras

COMPOSITIO MATHEMATICA, 154(6), 1269–1305.

By: O. Iyama, N. Reading*, I. Reiten & H. Thomas*

co-author countries: Canada 🇨🇦

Contributors: O. Iyama, N. Reading*, I. Reiten & H. Thomas*

author keywords: preprojective algebra; Weyl group; weak order; tau-tilting theory; brick; join-irreducible element; lattice congruence
Sources: Web Of Science, ORCID
Added: August 6, 2018

2018 journal article

Universal Geometric Coefficients for the Four-Punctured Sphere

Annals of Combinatorics, 22(1), 1–44.

By: E. Barnard n, E. Meehan n, N. Reading n & S. Viel n

Contributors: E. Barnard n, E. Meehan n, N. Reading n & S. Viel n

Sources: Crossref, ORCID
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.

By: N. Reading n & D. Speyer*

Contributors: N. Reading n & D. Speyer*

Sources: ORCID, Crossref
Added: June 30, 2019

2016 journal article

Combinatorial Frameworks for Cluster Algebras

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016(1), 109–173.

By: N. Reading n & D. Speyer*

Contributors: N. Reading n & D. Speyer*

Sources: Web Of Science, ORCID
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.

By: R. Ehrenborg*, C. Klivans* & N. Reading n

Contributors: R. Ehrenborg*, C. Klivans* & N. Reading n

author keywords: Hyperplane arrangements; Finite Coxeter systems; Spherical geometry
Sources: Crossref, ORCID
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).

By: N. Reading n

Contributors: N. Reading n

Sources: Crossref, ORCID
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).

By: N. Reading n

Contributors: N. Reading n

Sources: Crossref, ORCID
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

By: N. Reading & D. Speyer

Contributors: N. Reading & D. Speyer

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2015 journal article

Coxeter-biCatalan combinatorics

Discrete Mathematics & Theoretical Computer Science.

By: E. Barnard n & N. Reading n

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.

By: N. Reading*

Contributors: N. Reading*

author keywords: canonical join representation; lattice congruence; noncrossing arc diagram; permutation; weak order
Sources: Web Of Science, ORCID
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

By: N. Reading

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.

By: N. Reading n

Contributors: N. Reading n

Sources: Web Of Science, ORCID
Added: August 6, 2018

2014 journal article

Universal geometric cluster algebras

MATHEMATISCHE ZEITSCHRIFT, 277(1-2), 499–547.

By: N. Reading n

Contributors: N. Reading n

Sources: Web Of Science, ORCID
Added: August 6, 2018

2012 journal article

Coarsening polyhedral complexes

Proc. Amer. Math. Soc., 140(10), 3593–3605.

By: N. Reading n

Contributors: N. Reading n

Sources: NC State University Libraries, ORCID
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).

By: N. Reading n

Contributors: N. Reading n

Ed(s): F. Mueller-Hoissen, J. Pallo & J. Stasheff

Sources: ORCID, Web Of Science
Added: December 4, 2019

2012 journal article

Generic rectangulations

European Journal of Combinatorics, 33(4), 610–623.

By: N. Reading*

Contributors: N. Reading*

Sources: Crossref, ORCID
Added: July 1, 2019

2012 journal article

The Hopf algebra of diagonal rectangulations

JOURNAL OF COMBINATORIAL THEORY SERIES A, 119(3), 788–824.

By: S. Law n & N. Reading n

Contributors: S. Law n & N. Reading n

author keywords: Baxter permutation; Diagonal rectangulation; Hopf algebra
Sources: Web Of Science, ORCID
Added: August 6, 2018

2011 journal article

Noncrossing partitions and the shard intersection order

JOURNAL OF ALGEBRAIC COMBINATORICS, 33(4), 483–530.

By: N. Reading n

Contributors: N. Reading n

author keywords: Noncrossing partition; Shard; Coxeter group; Weak order
Sources: Web Of Science, ORCID
Added: August 6, 2018

2011 journal article

SORTABLE ELEMENTS IN INFINITE COXETER GROUPS

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(2), 699–761.

By: N. Reading n & D. Spoyer

Contributors: N. Reading n & D. Speyer*

Sources: Web Of Science, ORCID
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

By: N. Reading

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.

By: N. Reading n & D. Speyer n

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

By: N. Reading & D. Speyert

Contributors: N. Reading & D. Speyert

Source: ORCID
Added: January 16, 2020

2009 journal article

Cambrian fans

J. Eur. Math. Soc. (JEMS), 11(2), 407–447.

By: N. Reading* & D. Speyer*

Contributors: N. Reading* & D. Speyer*

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2009 journal article

Noncrossing partitions and the shard intersection order

Discrete Mathematics & Theoretical Computer Science.

By: N. Reading*

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

By: N. Reading

Contributors: N. Reading

Source: ORCID
Added: January 16, 2020

2008 journal article

Chains in the noncrossing partition lattice

SIAM JOURNAL ON DISCRETE MATHEMATICS, 22(3), 875–886.

By: N. Reading*

Contributors: N. Reading*

author keywords: absolute order; Catalan number; chain enumeration; Coxeter element; Coxeter group; generalized cluster complex; noncrossing partition; parking function
Sources: Web Of Science, ORCID
Added: August 6, 2018

2007 journal article

Clusters, coxeter-sortable elements and noncrossing partitions

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 359(12), 5931–5958.

By: N. Reading n

Contributors: N. Reading n

Sources: Web Of Science, ORCID
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

By: N. Reading

Contributors: N. Reading

Source: ORCID
Added: January 16, 2020

2007 chapter

Root systems and generalized associahedra

In Geometric Combinatorics (Vol. 13, pp. 63–131).

By: S. Fomin & N. Reading*

Sources: Crossref, ORCID
Added: July 1, 2019

2007 journal article

Sortable elements and Cambrian lattices

ALGEBRA UNIVERSALIS, 56(3-4), 411–437.

By: N. Reading*

Contributors: N. Reading*

Sources: Web Of Science, ORCID
Added: August 6, 2018

2006 journal article

Cambrian lattices

Advances in Mathematics, 205(2), 313–353.

By: N. Reading*

Contributors: N. Reading*

author keywords: cluster; Coxeter group; fiber polytope; generalized associahedron; lattice congruence; lattice quotient; Tamari lattice
Sources: Crossref, ORCID
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

By: N. Reading

Contributors: N. Reading

Source: ORCID
Added: January 16, 2020

2005 journal article

Generalized cluster complexes and Coxeter combinatorics

International Mathematics Research Notices, 2005(44), 2709–2757.

By: S. Fomin & N. Reading*

Contributors: S. Fomin & N. Reading*

Sources: ORCID, 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.

By: N. Reading*

Contributors: N. Reading*

author keywords: Coexter group; fan poset; hyperplane arrangement; Malvenuto-Reutenauer Hopf algebra; pattern avoidance; permutohedron; poset of regions; weak order
Sources: Crossref, ORCID
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

By: N. Reading & D. Waugh

Contributors: N. Reading & D. Waugh

Sources: NC State University Libraries, ORCID
Added: July 10, 2019

2004 journal article

Lattice Congruences of the Weak Order

Order, 21(4), 315–344.

By: N. Reading*

Contributors: N. Reading*

author keywords: Cambrian lattice; congruence uniform; Coxeter group; parabolic subgroup; poset of regions; shard; simplicial hyperplane arrangement; Tamari lattice; weak order
Sources: Crossref, ORCID
Added: July 1, 2019

2004 journal article

Non-negative cd-coefficients of Gorenstein∗ posets

Discrete Mathematics, 274(1-3), 323–329.

By: N. Reading*

Contributors: N. Reading*

author keywords: cd-index; Charney-Davis conjecture; eulerian poset; flag f-vector; Gorenstein
Sources: Crossref, ORCID
Added: July 1, 2019

2004 journal article

The cd-index of Bruhat intervals

The Electronic Journal of Combinatorics, 11(1), R74.

By: N. Reading*

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

By: N. Reading

Contributors: N. Reading

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.

By: N. Reading*

Contributors: N. Reading*

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
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.

By: N. Reading*

Contributors: N. Reading*

Sources: Crossref, ORCID
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

By: N. Reading

Source: ORCID
Added: December 4, 2019

2002 journal article

Order Dimension, Strong Bruhat Order and Lattice Properties for Posets

Order, 19(1), 73–100.

By: N. Reading*

Contributors: N. Reading*

author keywords: Bruhat; clivage; congruence; Coxeter; critical complex; Dilworth; dissective; distributive lattice; MacNeille completion; monotone triangle; order dimension
Sources: ORCID, Web Of Science
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

By: N. Reading

Contributors: N. Reading

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

By: D. Gibbon, K. Kennedy, N. Reading & M. Quieroz

Contributors: D. Gibbon, K. Kennedy, N. Reading & M. Quieroz

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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