Volume 13, issue 6 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Irreducibility of $q$–difference operators and the knot $7_4$

Stavros Garoufalidis and Christoph Koutschan

Algebraic & Geometric Topology 13 (2013) 3261–3286
1 S A Abramov, P Paule, M Petkovšek, $q$–hypergeometric solutions of $q$–difference equations, from: "Proceedings of the 7th Conference on Formal Power Series and Algebraic Combinatorics", Discrete Math. 180 (1998) 3 MR1603685
2 D Bar-Natan, The Knot Atlas
3 M Bronstein, On the factorisation of linear ordinary differential operators, from: "Symbolic computation, new trends and developments", Math. Comput. Simulation 42 (1996) 387 MR1430826
4 M Bronstein, M Petkovšek, An introduction to pseudo-linear algebra, from: "Algorithmic complexity of algebraic and geometric models", Theoret. Comput. Sci. 157 (1996) 3 MR1383396
5 F Chyzak, An extension of Zeilberger's fast algorithm to general holonomic functions, from: "Formal power series and algebraic combinatorics", Discrete Math. 217 (2000) 115 MR1766263
6 T Cluzeau, M van Hoeij, Computing hypergeometric solutions of linear recurrence equations, Appl. Algebra Engrg. Comm. Comput. 17 (2006) 83 MR2233774
7 D Cooper, M Culler, H Gillet, D D Long, P B Shalen, Plane curves associated to character varieties of $3$–manifolds, Invent. Math. 118 (1994) 47 MR1288467
8 J A De Loera, J Rambau, F Santos, Triangulations, Algorithms and Computation in Mathematics 25, Springer (2010) MR2743368
9 S Garoufalidis, The classical and quantum $A$–polynomial of double twist knots
10 S Garoufalidis, The Newton polygon of a recurrence sequence of polynomials and its role in TQFT arXiv:1102.1346
11 S Garoufalidis, Quantum knot invariants arXiv:1201.3314
12 S Garoufalidis, On the characteristic and deformation varieties of a knot, from: "Proceedings of the Casson Fest", Geom. Topol. Monogr. 7 (2004) 291 MR2172488
13 S Garoufalidis, The degree of a $q$–holonomic sequence is a quadratic quasi-polynomial, Electron. J. Combin. 18 (2011) 23 MR2795781
14 S Garoufalidis, The Jones slopes of a knot, Quantum Topol. 2 (2011) 43 MR2763086
15 S Garoufalidis, T T Q Lê, The colored Jones function is $q$–holonomic, Geom. Topol. 9 (2005) 1253 MR2174266
16 S Garoufalidis, X Sun, The $C$–polynomial of a knot, Algebr. Geom. Topol. 6 (2006) 1623 MR2253459
17 S Garoufalidis, X Sun, The non-commutative $A$–polynomial of twist knots, J. Knot Theory Ramifications 19 (2010) 1571 MR2755491
18 R Gelca, On the relation between the $A$–polynomial and the Jones polynomial, Proc. Amer. Math. Soc. 130 (2002) 1235 MR1873802
19 K Habiro, A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres, Invent. Math. 171 (2008) 1 MR2358055
20 M van Hoeij, Factorization of differential operators with rational functions coefficients, J. Symbolic Comput. 24 (1997) 537 MR1484068
21 P Horn, Faktorisierung in Schief-Polynomringen, PhD thesis, Universität Kassel (2008)
22 J C Jantzen, Lectures on quantum groups, Graduate Studies in Mathematics 6, Amer. Math. Soc. (1996) MR1359532
23 C Koutschan, Advanced applications of the holonomic systems approach, PhD thesis, Johannes Kepler University (2009)
24 C Koutschan, A fast approach to creative telescoping, Math. Comput. Sci. 4 (2010) 259 MR2775992
25 C Koutschan, HolonomicFunctions (user's guide), (2010)
26 M Lauridsen, Aspects of quantum mathematics, Hitchin connections and AJ conjectures, PhD thesis, Aarhus University (2010)
27 T T Q Lê, The colored Jones polynomial and the $A$–polynomial of knots, Adv. Math. 207 (2006) 782 MR2271986
28 T T Q Lê, A T Tran, On the AJ conjecture for knots arXiv:1111.5258
29 I G Macdonald, Symmetric functions and Hall polynomials, Oxford University Press (1995) MR1354144
30 G Masbaum, Skein-theoretical derivation of some formulas of Habiro, Algebr. Geom. Topol. 3 (2003) 537 MR1997328
31 O Ore, Theory of non-commutative polynomials, Ann. of Math. 34 (1933) 480 MR1503119
32 P Paule, A Riese, A Mathematica $q$–analogue of Zeilberger's algorithm based on an algebraically motivated approach to $q$–hypergeometric telescoping, from: "Special functions, $q$–series and related topics" (editors M E H Ismail, D R Masson, M Rahman), Fields Inst. Commun. 14, Amer. Math. Soc. (1997) 179 MR1448687
33 K L Petersen, $A$–polynomials of a family of $2$–bridge knots, preprint (2011)
34 M Petkovšek, Hypergeometric solutions of linear recurrences with polynomial coefficients, J. Symbolic Comput. 14 (1992) 243 MR1187234
35 M Petkovšek, H S Wilf, D Zeilberger, $A=B$, A K Peters Ltd (1996) MR1379802
36 M van der Put, M F Singer, Galois theory of linear differential equations, Grundl. Math. Wissen. 328, Springer (2003) MR1960772
37 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish Inc (1990) MR1277811
38 F Schwarz, A factorization algorithm for linear ordinary differential equations, from: "ISSAC 1989—Proceedings of the 1989 International Symposium on Symbolic and Algebraic Computation" (editor Y N Lakshman), ACM Press (1989) 17
39 J R Stembridge, The SF package (2005)
40 S P Tsarev, An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator, from: "ISSAC 1996—Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation" (editor Y N Lakshman), ACM Press (1996) 226
41 V G Turaev, The Yang–Baxter equation and invariants of links, Invent. Math. 92 (1988) 527 MR939474
42 V G Turaev, Quantum invariants of knots and $3$–manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673
43 H S Wilf, D Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and “$q$”) multisum/integral identities, Invent. Math. 108 (1992) 575 MR1163239
44 D Zeilberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (1990) 207 MR1048463
45 D Zeilberger, A holonomic systems approach to special functions identities, J. Comput. Appl. Math. 32 (1990) 321 MR1090884
46 D Zeilberger, The method of creative telescoping, J. Symbolic Comput. 11 (1991) 195 MR1103727
47 G M Ziegler, Lectures on polytopes, Graduate Texts in Mathematics 152, Springer (1995) MR1311028