101 citations · 629 across the 59 of their papers we have counts for
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Irreducibility of q-difference operators and the knot 7_4
Stavros Garoufalidis, Christoph Koutschan
Our goal is to compute the minimal-order recurrence of the colored Jones polynomial of the 7_4 knot, as well as for the first four double twist knots. As a corollary, we verify the…
Twisting q-holonomic sequences by complex roots of unity
Stavros Garoufalidis, Christoph Koutschan
A sequence is -holonomic if it satisfies a nontrivial linear recurrence with coefficients polynomials in and . Our main theorems state that -holonomicity is…
The non-commutative A-polynomial of (-2,3,n) pretzel knots
Stavros Garoufalidis, Christoph Koutschan
We study q-holonomic sequences that arise as the colored Jones polynomial of knots in 3-space. The minimal-order recurrence for such a sequence is called the (non-commutative) A-po…
The SL_3 Jones polynomial of the trefoil: a case study of -holonomic sequences
Stavros Garoufalidis, Christoph Koutschan
The SL_3 colored Jones polynomial of the trefoil knot is a -holonomic sequence of two variables with natural origin, namely quantum topology. The paper presents an explicit set…