Updated: November 1st, 2024 14:40

2022 article

DOMINANCE PHENOMENA: MUTATION, SCATTERING AND CLUSTER ALGEBRAS

Reading, N. (2022, October 28). *TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY*, Vol. 10.

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*.

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: ORCID

Added: April 28, 2020

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

Lattice structure of Weyl groups via representation theory of preprojective algebras

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

Contributors: O. Iyama^{*}, ^{ n} , I. Reiten & H. Thomas ^{*}

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

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

2018 journal article

Universal Geometric Coefficients for the Four-Punctured Sphere

*Annals of Combinatorics*, *22*(1), 1–44.

Contributors: E. Barnard^{ n}, E. Meehan^{ n}, ^{ n} & S. Viel ^{ n}

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

2017 journal article

Coxeter-biCatalan combinatorics

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

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

2017 journal article

INITIAL-SEED RECURSIONS AND DUALITIES FOR d-VECTORS

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

Contributors: ^{ n} & S. Stella ^{*}

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

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

Combinatorial Frameworks for Cluster Algebras

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

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

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

Universal geometric cluster algebras

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

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

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Sources: Crossref, ORCID, NC State University Libraries

Added: July 1, 2019

2011 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

2010 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

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 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

Sortable elements for quivers with cycles

*The Electronic Journal of Combinatorics*, *17*(1), R90.

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 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

Sources: Crossref, ORCID, NC State University Libraries

Added: July 1, 2019

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

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

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

2004 journal article

The cd-index of Bruhat intervals

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

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.

Sources: Crossref, ORCID, NC State University Libraries

Added: July 1, 2019

2003 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

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.

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

Updated: January 6th, 2020 11:03

2018 - present

2012 - 2018

2006 - 2012

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