Algebraic & Geometric Topology Volume 13, issue 6 (2013)

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Irreducibility of $q$–difference operators and the knot $7_4$

Stavros Garoufalidis and Christoph Koutschan

Algebraic & Geometric Topology 13 (2013) 3261–3286

DOI: 10.2140/agt.2013.13.3261

Bibliography

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