Skip to main content
  • Submit
  • About
    • Editorial Board
    • PNAS Staff
    • FAQ
    • Accessibility Statement
    • Rights and Permissions
    • Site Map
  • Contact
  • Journal Club
  • Subscribe
    • Subscription Rates
    • Subscriptions FAQ
    • Open Access
    • Recommend PNAS to Your Librarian
  • Log in
  • My Cart

Main menu

  • Home
  • Articles
    • Current
    • Special Feature Articles - Most Recent
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • List of Issues
  • Front Matter
  • News
    • For the Press
    • This Week In PNAS
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Editorial and Journal Policies
    • Submission Procedures
    • Fees and Licenses
  • Submit
  • About
    • Editorial Board
    • PNAS Staff
    • FAQ
    • Accessibility Statement
    • Rights and Permissions
    • Site Map
  • Contact
  • Journal Club
  • Subscribe
    • Subscription Rates
    • Subscriptions FAQ
    • Open Access
    • Recommend PNAS to Your Librarian

User menu

  • Log in
  • My Cart

Search

  • Advanced search
Home
Home

Advanced Search

  • Home
  • Articles
    • Current
    • Special Feature Articles - Most Recent
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • List of Issues
  • Front Matter
  • News
    • For the Press
    • This Week In PNAS
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Editorial and Journal Policies
    • Submission Procedures
    • Fees and Licenses

New Research In

Physical Sciences

Featured Portals

  • Physics
  • Chemistry
  • Sustainability Science

Articles by Topic

  • Applied Mathematics
  • Applied Physical Sciences
  • Astronomy
  • Computer Sciences
  • Earth, Atmospheric, and Planetary Sciences
  • Engineering
  • Environmental Sciences
  • Mathematics
  • Statistics

Social Sciences

Featured Portals

  • Anthropology
  • Sustainability Science

Articles by Topic

  • Economic Sciences
  • Environmental Sciences
  • Political Sciences
  • Psychological and Cognitive Sciences
  • Social Sciences

Biological Sciences

Featured Portals

  • Sustainability Science

Articles by Topic

  • Agricultural Sciences
  • Anthropology
  • Applied Biological Sciences
  • Biochemistry
  • Biophysics and Computational Biology
  • Cell Biology
  • Developmental Biology
  • Ecology
  • Environmental Sciences
  • Evolution
  • Genetics
  • Immunology and Inflammation
  • Medical Sciences
  • Microbiology
  • Neuroscience
  • Pharmacology
  • Physiology
  • Plant Biology
  • Population Biology
  • Psychological and Cognitive Sciences
  • Sustainability Science
  • Systems Biology
Research Article

The quantum MacMahon Master Theorem

Stavros Garoufalidis, Thang T. Q. Lê, and Doron Zeilberger
PNAS September 19, 2006 103 (38) 13928-13931; https://doi.org/10.1073/pnas.0606003103
Stavros Garoufalidis
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: stavros@math.gatech.edu
Thang T. Q. Lê
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Doron Zeilberger
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  1. Edited by Robion C. Kirby, University of California, Berkeley, CA, and approved July 24, 2006 (received for review July 17, 2006)

  • Article
  • Info & Metrics
  • PDF
Loading

Online Impact

 

Article Information

vol. 103 no. 38 13928-13931
DOI: 
https://doi.org/10.1073/pnas.0606003103
PubMed: 
16966614

Published By: 
National Academy of Sciences
Print ISSN: 
0027-8424
Online ISSN: 
1091-6490
History: 
  • Published in issue September 19, 2006.
  • Published first September 11, 2006.

Copyright & Usage: 
© 2006 by The National Academy of Sciences of the USA

Author Information

  1. Stavros Garoufalidis * , † ,
  2. Thang T. Q. Lê *, and
  3. Doron Zeilberger ‡
  1. *School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160; and
  2. ‡Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019
  1. Edited by Robion C. Kirby, University of California, Berkeley, CA, and approved July 24, 2006 (received for review July 17, 2006)

Footnotes

  • †To whom correspondence should be addressed. E-mail: stavros{at}math.gatech.edu
  • Author contributions: S.G., T.T.Q.L., and D.Z. performed research.

  • The authors declare no conflict of interest.

  • This paper was submitted directly (Track II) to the PNAS office.

  • © 2006 by The National Academy of Sciences of the USA

Cited By...

  • 18 Citations
  • 17 Citations
  • Google Scholar

This article has been cited by the following articles in journals that are participating in Crossref Cited-by Linking.

  • The colored Jones function is q-holonomic
    Stavros Garoufalidis, Thang T Q Le
    Geometry & Topology 2005 9 3
  • Algebraic properties of Manin matrices 1
    A. Chervov, G. Falqui, V. Rubtsov
    Advances in Applied Mathematics 2009 43 3
  • A class of left quantum groups modeled after <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mstyle mathvariant="normal"><mml:mi>SL</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
    Aaron Lauve, Earl J. Taft
    Journal of Pure and Applied Algebra 2007 208 3
  • On Higher-Order Sugawara Operators
    A. V. Chervov, A. I. Molev
    International Mathematics Research Notices 2009
  • Center of the quantum affine vertex algebra in type A
    Naihuan Jing, Slaven Kožić, Alexander Molev, Fan Yang
    Journal of Algebra 2018 496
  • Extended MacMahon–Schwingerʼs Master Theorem and conformal wavelets in complex Minkowski space
    M. Calixto, E. Pérez-Romero
    Applied and Computational Harmonic Analysis 2011 31 1
  • A new proof of the Garoufalidis–Lê–Zeilberger quantum MacMahon Master Theorem
    Dominique Foata, Guo-Niu Han
    Journal of Algebra 2007 307 1
  • Algebraic properties of Manin matrices II: q-analogues and integrable systems
    A. Chervov, G. Falqui, V. Rubtsov, A. Silantyev
    Advances in Applied Mathematics 2014 60
  • Non-commutative extensions of the MacMahon Master Theorem
    Matjaž Konvalinka, Igor Pak
    Advances in Mathematics 2007 216 1
  • Quantization of the shift of argument subalgebras in type A
    Vyacheslav Futorny, Alexander Molev
    Advances in Mathematics 2015 285
  • A basis for the right quantum algebra and the “1=q” principle
    Dominique Foata, Guo-Niu Han
    Journal of Algebraic Combinatorics 2008 27 2
  • Eigenvalues of Bethe vectors in the Gaudin model
    A. I. Molev, E. E. Mukhin
    Theoretical and Mathematical Physics 2017 192 3
  • One-sided Hopf algebras and quantum quasigroups
    Uma N. Iyer, Jonathan D. H. Smith, Earl J. Taft
    Communications in Algebra 2018 46 11
  • Specializations and extensions of the quantum MacMahon Master Theorem
    Dominique Foata, Guo-Niu Han
    Linear Algebra and its Applications 2007 423 2-3
  • COMBINATORICS AND N-KOSZUL ALGEBRAS
    ROLAND BERGER
    International Journal of Geometric Methods in Modern Physics 2008 05 08
  • Some generalizations of the MacMahon Master Theorem
    Michael P. Tuite
    Journal of Combinatorial Theory, Series A 2013 120 1
  • Собственные значения векторов Бете в модели Годена
    Александр Иванович Молев, Alexander Ivanovich Molev, Евгений Евгеньевич Мухин, Evgenii Evgen'evich Mukhin
    Теоретическая и математическая физика 2017 192 3

Article usage

Article usage: September 2006 to January 2021

AbstractFullPdf
Sep 200650096209
Oct 2006621825
Nov 200616910
Dec 20061134
Total 2006589126248
Jan 20071967
Feb 20071151
Mar 200710137
Apr 20075113
May 20073613
Jun 2007227
Jul 2007415
Aug 20077910
Sep 200781114
Oct 2007112518
Nov 200731310
Dec 20072158
Total 200785117103
Jan 200851513
Feb 200811111
Mar 2008595
Apr 200881214
May 200822826
Jun 2008161416
Jul 20082043
Aug 200817114
Sep 200832125
Oct 200836169
Nov 20084687
Dec 20082264
Total 2008230126117
Jan 20091875
Feb 20092094
Mar 200917124
Apr 2009201213
May 20091583
Jun 20092658
Jul 20092265
Aug 20091352
Sep 200917941
Oct 20093088
Nov 2009169501
Dec 200911101
Total 2009225100595
Jan 201022125
Feb 20101626
Mar 201024144
Apr 20101474
May 201012124
Jun 20101322
Jul 2010742
Aug 20101482
Sep 201022104
Oct 20101452
Nov 201015132
Dec 20101540
Total 20101889337
Jan 20111191
Feb 2011832
Mar 201124141
Apr 2011640
May 201112147
Jun 201110204
Jul 201119156
Aug 20112272
Sep 20112289
Oct 201136226
Nov 2011312211
Dec 20111871
Total 201121914550
Jan 20122284
Feb 20124451
Mar 201231910
Apr 20122974
May 201222142
Jun 201236107
Jul 201214486
Aug 201211121
Sep 20121275
Oct 201216111
Nov 20121983
Dec 20122253
Total 201227814447
Jan 201327130
Feb 20131962
Mar 201334138
Apr 20132685
May 20132664
Jun 201318112
Jul 2013731
Aug 20132222
Sep 20131230
Oct 20133273
Nov 20131531
Dec 201311137
Total 20132498835
Jan 20141461
Feb 201414144
Mar 20141651
Apr 20142093
May 20141882
Jun 20141253
Jul 201415111
Aug 20141393
Sep 20141351
Oct 20148143
Nov 20144203
Dec 20147114
Total 201415411729
Jan 2015450
Feb 2015973
Mar 201514124
Apr 20151393
May 20157113
Jun 2015712
Jul 2015431
Aug 201513158
Sep 2015185
Oct 2015953
Nov 20151173
Dec 20151178
Total 20151039043
Jan 2016979
Feb 20161575
Mar 20162288
Apr 2016534
May 201611104
Jun 2016641
Jul 20161853
Aug 201628184
Sep 201615331
Oct 201612362
Nov 201612342
Dec 201612243
Total 201616518946
Jan 20175374
Feb 201711313
Mar 20176405
Apr 20175401
May 20171182
Jun 20171085
Jul 20178411
Aug 20175145
Sep 20178104
Oct 20178135
Nov 20175114
Dec 20174115
Total 20178622754
Jan 20189102
Feb 201882410
Mar 201812168
Apr 2018142410
May 201818294
Jun 201814225
Jul 20185114
Aug 201815212
Sep 201812213
Oct 201811712
Nov 20180146
Dec 20180172
Total 201810822668
Jan 20190110
Feb 20192174
Mar 201911110
Apr 20192176
May 20190161
Jun 20190207
Jul 20190168
Aug 20190156
Sep 2019092
Oct 20192174
Nov 20190205
Dec 20191174
Total 2019818657
Jan 20200241
Feb 20200146
Mar 20201152
Apr 20200101
May 20200172
Jun 2020173
Jul 20200111
Aug 20200229
Sep 20201185
Oct 202022110
Nov 202052912
Dec 20204278
Total 20201421560
Jan 202111710
Total 202111710
Total270222061599
PreviousNext
Back to top
Article Alerts
Email Article

Thank you for your interest in spreading the word on PNAS.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
The quantum MacMahon Master Theorem
(Your Name) has sent you a message from PNAS
(Your Name) thought you would like to see the PNAS web site.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Citation Tools
The quantum MacMahon Master Theorem
Stavros Garoufalidis, Thang T. Q. Lê, Doron Zeilberger
Proceedings of the National Academy of Sciences Sep 2006, 103 (38) 13928-13931; DOI: 10.1073/pnas.0606003103

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Request Permissions
Share
The quantum MacMahon Master Theorem
Stavros Garoufalidis, Thang T. Q. Lê, Doron Zeilberger
Proceedings of the National Academy of Sciences Sep 2006, 103 (38) 13928-13931; DOI: 10.1073/pnas.0606003103
Digg logo Reddit logo Twitter logo Facebook logo Google logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Mendeley logo Mendeley
Proceedings of the National Academy of Sciences: 103 (38)
Table of Contents

Submit

Sign up for Article Alerts

Jump to section

  • Article
    • Abstract
    • MacMahon's Master Theorem
    • Quantum Algebra, Right-Quantum Matrices, and Quantum Determinants
    • A q-Version of MacMahon's Master Theorem
    • Computer Code
    • Proof
    • Some Remarks on the Boson–Fermion Correspondence
    • Acknowledgments
    • Footnotes
    • References
  • Info & Metrics
  • PDF

You May Also be Interested in

Abstract depiction of a guitar and musical note
Science & Culture: At the nexus of music and medicine, some see disease treatments
Although the evidence is still limited, a growing body of research suggests music may have beneficial effects for diseases such as Parkinson’s.
Image credit: Shutterstock/agsandrew.
Scientist looking at an electronic tablet
Opinion: Standardizing gene product nomenclature—a call to action
Biomedical communities and journals need to standardize nomenclature of gene products to enhance accuracy in scientific and public communication.
Image credit: Shutterstock/greenbutterfly.
One red and one yellow modeled protein structures
Journal Club: Study reveals evolutionary origins of fold-switching protein
Shapeshifting designs could have wide-ranging pharmaceutical and biomedical applications in coming years.
Image credit: Acacia Dishman/Medical College of Wisconsin.
White and blue bird
Hazards of ozone pollution to birds
Amanda Rodewald, Ivan Rudik, and Catherine Kling talk about the hazards of ozone pollution to birds.
Listen
Past PodcastsSubscribe
Goats standing in a pin
Transplantation of sperm-producing stem cells
CRISPR-Cas9 gene editing can improve the effectiveness of spermatogonial stem cell transplantation in mice and livestock, a study finds.
Image credit: Jon M. Oatley.

Similar Articles

Site Logo
Powered by HighWire
  • Submit Manuscript
  • Twitter
  • Facebook
  • RSS Feeds
  • Email Alerts

Articles

  • Current Issue
  • Latest Articles
  • Archive

PNAS Portals

  • Anthropology
  • Chemistry
  • Classics
  • Front Matter
  • Physics
  • Sustainability Science
  • Teaching Resources

Information

  • Authors
  • Editorial Board
  • Reviewers
  • Librarians
  • Press
  • Site Map
  • PNAS Updates

Feedback    Privacy/Legal

Copyright © 2021 National Academy of Sciences. Online ISSN 1091-6490