UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)
UvA-DARE (Digital Academic Repository)
Graph parameters and invariants of the orthogonal group
Regts, G.
Publication date
2013
Link to publication
Citation for published version (APA):
Regts, G. (2013). Graph parameters and invariants of the orthogonal group.
General rights
It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).
Disclaimer/Complaints regulations
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
[1] I.V. Arzhantsev: Invariant ideals and Matsushima’s criterion, Communica-tions in Algebra 36 (2008), 4368–4374.
[2] L. Beaudin, J. Ellis-Monaghan, G. Pangborn and R. Shrock: A little sta-tistical mechanics for the graph theorist, Discrete Mathematics 310 (2010), 2037–2053.
[3] D. Birkes: Orbits of linear algebraic groups, Annals of Mathematics Second Series 93 (1971), 459–475.
[4] A. Borel: Linear Algebraic Groups, Springer, New York, 1991.
[5] C. Borgs, J. Chayes, L. Lovász, V.T. Sós, B. Szegedy and K. Vesztergombi: Graph limits and parameter testing, Proceedings of the 37th Annual ACM Symposium on Theory of Computing (2006), 261–270.
[6] C. Borgs, J. Chayes, L. Lovász, V.T. Sós and K. Vesztergombi: Counting graph homomorphisms, in: Topics in Discrete Mathematics (eds. M. Klazar, J. Kratochvil, M. Loebl, J. Matou˘sek, R. Thomas, P. Valtr), Springer (2006), 315–371.
[7] C. Borgs, J. Chayes, L. Lovász, V.T. Sós and K. Vesztergombi: Convergent graph sequences I: Subgraph frequencies, metric properties and testing, Advances in Mathematics 219 (2008), 1801–1851.
[8] R. Brauer: On algebras which are Connected with the semisimple contin-uous groups, Annals of Mathematics Second Series 38 (1937), 857–872. [9] M. Brion: Introduction to actions of algebraic groups, Les cours du CIRM 1
(2010), 1–22.
[10] A. Bulatov and M. Grohe: The complexity of partition functions, Theoretical Computer Science 348 (2005), 148–186.
BIBLIOGRAPHY
[11] J.Y. Cai, X. Chen and P. Lu: Graph homomorphisms with complex values: A dichotomy theorem, in: Automata, Languages and Programming, Springer, Berlin Heidelberg (2010), 275–286.
[12] J.Y. Cai, P. Lu and M. Xia: Holant problems and counting CSP, Proceedings of the 41stannual ACM Symposium on Theory of Computing (2009), 715–724. [13] J.Y. Cai, P. Lu and M. Xia: Computational complexity of holant problems,
SIAM Journal on Computing 40 (2011), 1101–1132.
[14] A. Conca: Gröbner bases of ideals of minors of a symmetric matrix, Journal of Algebra 166 (1994), 406–421.
[15] J.B. Conway: A Course in Functional Analysis, Second edition, Graduate Texts in Mathematics 96, Springer, New York, 2007.
[16] D.A. Cox, J. Little and D. O’Shea: Ideals, Varieties, and Algorithms: An Intro-duction to Computational Algebraic Geometry and Commutative Algebra, Un-dergraduate Texts in Mathematics 10, Springer Verlag, 2007.
[17] D.A. Cox, J. Little and D. O’Shea: Using Algebraic Geometry, Second Edi-tion, Graduate Texts in Mathematics 185, Springer, New York, 2004. [18] P. Diaconis and S. Janson: Graph limits and exchangeable random graphs,
Rendiconti di Matematica 28 (2008), 33–61.
[19] J. Draisma, D. Gijswijt, L. Lovász, G. Regts and A. Schrijver: Characteriz-ing partition functions of the vertex model, Journal of Algebra 350 (2012), 197–206.
[20] J. Draisma and G. Regts: Tensor invariants for certain subgroups of the orthogonal group, Journal of Algebraic Combinatorics 38 (2013), 393–405. [21] M. Dyer and C. Greenhill: The complexity of counting graph
homomor-phisms, in: Proceedings of the eleventh annual ACM-SIAM Symposium on Dis-crete Algorithms (2000), 246–255.
[22] P. Erdös, L. Lovász and J. Spencer: Strong independence of graphcopy functions, in: Graph Theory and Related Topics, Academic Press (1979), 165– 172.
[23] W. Fernandez de la Vega, R. Kannan, M. Karpinski and S. Vempala: Ten-sor decomposition and approximation schemes for constraint satisfaction problems, in: Proceedings of the 37th Annual ACM Symposium on Theory of Computing (2005), 747–754.
[24] M. Freedman, L. Lovász and A. Schrijver: Reflection positivity, rank con-nectivity, and homomorphisms of graphs, Journal of the American Mathe-matical Society 20 37–51, 2007.
[25] R. Goodman and N.R. Wallach: Symmetry, Representations and Invariants, Graduate Texts in Mathematics 255, Springer, Dordrecht, 2009.
[26] P. Hanlon and D. Wales: On the decomposition of Brauer’s centralizer algebra, Journal of Algebra 121 (1989), 409–445.
[27] F. Harary: Graph Theory, Addison-Wesley, Reading M.A., 1971.
[28] P. de la Harpe and V.F.R. Jones: Graph invariants related to statistical me-chanical models: examples and problems, Journal of Combinatorial Theory Series B 57 (1993), 207–227.
[29] A.K. Hartmann and M. Weigt: Phase Transitions in Combinatorial Optimiza-tion Problems: Basics, Algorithms and Statistical Mechanics. Wiley-Vch, Wein-heim, 2006.
[30] J.E. Humphreys: Linear Algebraic Groups, Graduate Texts in Mathematics 21, Springer Verlag, New York, 1975.
[31] R. Kannan: Spectral methods for matrices and tensors, in: Proceedings of the 42nd ACM Symposium on Theory of Computing (2010), 1–12. (preprint available at http://arxiv.org/pdf/1004.1253.pdf)
[32] G. Kempf: Instability in invariant theory, Annals of Mathematics Second Series 108 (1978), 299–316.
[33] G. Kempf and L. Ness: The length of vectors in representation spaces, in: Algebraic Geometry, Summer Meeting, Copenhagen, August 7–12, 1978, Lecture Notes in Mathematics 732 (1979), Springer Berlin, 233–243.
[34] H. Kraft: Geometrische Methoden in der Invariantentheorie, Vieweg, Braun-schweig, 1984.
[35] H. Kraft and C. Procesi: Classical Invariant Theory, A Primer, preprint, http://jones.math.unibas.ch/ kraft/Papers/KP-Primer.pdf
[36] S. Lang: Algebra, Revised Third Edition, Graduate Texts in Mathematics 211, Springer Verlag, New York, 2005.
[37] S. Lang: Hilbert’s Nullstellensatz in infinite-dimensional space, Proceedings of the American Mathematical Society 3 (1952), 407–410.
BIBLIOGRAPHY
[38] L. Lovász: Connection matrices, in: Combinatorics, Complexity, and Chance, A Tribute to Dominic Welsh, eds. G. Grimmet and C. McDiarmid, Oxford Univ. Press (2007), 179–190.
[39] L. Lovász: Graph homomorphisms: Open problems, manuscript available at http://www.cs.elte.hu/˜lovasz/problems.pdf, 2008.
[40] L. Lovász: Large Networks and Graph Limits, American Mathematical Soci-ety, Providence, Rhode Island, 2012.
[41] L. Lovász: The rank of connection matrices and the dimension of graph algebras, European Journal of Combinatorics 27 (2006), 962–970.
[42] L. Lovász and A. Schrijver: Graph parameters and semigroup functions, European Journal of Combinatorics 29 (2008), 987–1002.
[43] L. Lovász and A. Schrijver: Semidefinite functions on categories, The Elec-tronic Journal of Combinatorics 16 (2009), no 2, Special volume in honor of Anders Björner, Research Paper 14, 16pp.
[44] L. Lovász and V. Sós: Generalized quasi random graphs, Journal of Combi-natorial Theory, Series B, 2008.
[45] L. Lovász and B. Szegedy: Limits of dense graph sequences Journal of Combinatorial Theory Series B 96 (2006), 933–957.
[46] L. Lovász and B. Szegedy: Szemerédi’s Lemma for the analyst, Journal of Geometric and Functional Analysis 17 (2007), 252–270.
[47] J. Makowsky: Connection matrices for msol-definable structural in-variants, in: Logic and Its Applications ICLA 2009 (eds. R. Ramanujam, S.Sarukkai), Springer, Berlin Heidelberg (2009), 51–64.
[48] I. L. Markov and Y. Shi: Simulating quantum computation by contracting tensor networks, SIAM Journal on Computing 38 (2008), 963–981.
[49] T. Nishiura: Measure-preserving maps of Rn, Real Analysis Exchange 24 (1998), 837–842.
[50] V.L. Popov and E.B. Vinberg: Invariant Theory, Part II of Algebraic geome-try IV: linear algebraic groups, invariant theory, Encyclopaedia of Mathe-matical Sciences 55, Springer Verlag, Berlin, 1994.
[52] A. Razborov: On the minimal density of triangles in graphs, Combinatorics, Probability and Computing 17 (2008), 603–618.
[53] G. Regts: The rank of edge connection matrices and the dimension of algebras of invariant tensors, European Journal of Combinatorics 33 (2012), 1167-1173.
[54] G. Regts: A characterization of edge-reflection positive parti-tion funcparti-tions of vertex-coloring models, preprint (2013), http:// arxiv.org/pdf/1302.6497.pdf, Extended abstract in: The Seventh Euro-pean Conference on Combinatorics, Graph Theory and Applications, Eurocomb 2013 (eds. J. Nešetˇril and M. Pellegrini), CRM Series 16, Springer (2013), 305–311.
[55] G. Regts and A. Schrijver: Compact orbit spaces in Hilbert spaces and limits of edge-colouring models, preprint (2012), http:// arxiv.org/pdf/1210.2204v1.pdf.
[56] M.H. Rosas and B.E. Sagan: Symmetric functions in noncommuting vari-ables, Transactions of the Amereican Mathematical Society 358 (2006), 183-214. [57] B.E. Sagan: The Symmetric group: Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd Edition, Graduate Texts in Mathematics 203, Springer-Verlag New York, 2001.
[58] A. Schrijver: Tensor subalgebras and first fundamental theorems in invari-ant theory, Journal of Algebra 319 (2008), 1305–1319.
[59] A. Schrijver: Graph invariants in the edge model. in: Building Bridges Be-tween Mathematics and Computer Science (eds. M. Grötschel, G.O.H. Katona), Springer, Berlin (2008), 487–498.
[60] A. Schrijver: Graph invariants in the spin model, Journal of Combinatorial Theory, Series B 99 (2009), 502–511.
[61] A. Schrijver: Characterizing partition functions of the spin model by rank growth, Indagationes Mathematicae (2013), http://dx.doi.org/10.1016/ j.indag.2013.04.004.
[62] A. Schrijver: Characterizing partition functions of the vertex model by rank growth, preprint (2012), http://arxiv.org/pdf/1211.3561v1.pdf. [63] A. Schrijver: Low rank approximation to polynomials, preprint (2012),
BIBLIOGRAPHY
[64] R.P. Stanley: Enumerative Combinatorics Vol. 2, Cambridge Studies in Ad-vanced Mathematics 62, Cambridge University Press, 1999.
[65] R.P. Stanley: Catalan Addendum, version of 25 May 2013, http:// www-math.mit.edu/˜rstan/ec/catadd.pdf.
[66] B. Szegedy: Edge coloring models and reflection positivity, Journal of the American Mathematical Society 20 (2007), 969–988.
[67] B. Szegedy: Edge coloring models as singular vertex-coloring models, in: Fete of Combinatorics and Computer Science (eds. G.O.H. Katona, A. Schrijver, T. Szönyi), Springer, Heidelberg and János Bolyai Mathematical Society, Budapest (2010), 327–336.
[68] G. Xin and J. Xu: A short approach to Catalan numbers modulo 2r, The Electronic Journal of Combinatorics 18 (2011), #P177.