Skew(2^e) equals (7 times 4 to the e-2 plus 8) divided by 6 for e at least 3, with the recurrence Skew(2^e) = 4 times Skew(2^{e-1}) minus 4 for e at least 4.
The Magma algebra system I: The user language,
15 Pith papers cite this work, alongside 14 external citations. Polarity classification is still indexing.
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2026 15representative citing papers
Explicit non-trivial elements in K_4^{(3)} of Fermat curves are built uniformly in N, with regulators expressed via Zagier's trilogarithm and hypergeometric functions, plus numerical checks of Beilinson conjectures for N=3,4,6.
Q_{4n} is an NCI-group for all n≥2, never an NNN-group, and an NNND-group precisely when n is even and ≥6.
SageMath-augmented ReAct agents raise solve rates by +9.7 pp on average on a curated 133-problem RealMath subset, with GPT-5.5 reaching 75.2%.
Defines a canonical labelling function for finite solvable groups via presentations and cohomology so that can(G) equals can(H) exactly when G and H are isomorphic.
Extends eventual stability of quadratic iterates f = x² + 1/c to Q(i) by proving the case c ≡ 2 mod 4 is stable, supporting a prior conjecture with an auxiliary check due to lack of ordering.
Extends classifications of hyperelliptic Atkin-Lehner quotients from modular curves (D=1) and trivial quotients to general Shimura curves with coprime level.
Analogues of Sylow's first, Cauchy's, and Hall's theorems are established for finite skew braces, with application to classification of order pq examples.
Structured Groebner basis search in a 40-dimensional self-equivalence subspace of functions over F_{2^8} yields 566 quadratic APN functions in six classes, four of which are absent from prior databases of millions of instances.
Classifies orbits of points, planes and lines under the stabilizer of the twisted cubic in PG(3,q) for q=2,3,4 and determines incidence matrices between the resulting orbit partitions.
An algorithm is provided for selecting distinguished defining polynomials for p-adic field extensions, serving as a key component in expanding the LMFDB p-adic fields database.
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
Authors classify arc-transitive inner-automorphic Cayley graphs on dihedral groups, supply a necessary condition plus infinite examples, and finish the 2-distance-transitive case.
A Julia F4 package with a reusable learn/apply tracing interface speeds up repeated Gröbner-basis computations, with 1.5–6.6x measured gains in solving and identifiability benchmarks.
Two optimizations to Jacobian arithmetic in global function fields—optimized reductions for typical cases and caching—yield faster practical performance with the first public software supporting unique divisor class representatives.
citing papers explorer
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Enumeration of skew morphisms of cyclic $2$-groups
Skew(2^e) equals (7 times 4 to the e-2 plus 8) divided by 6 for e at least 3, with the recurrence Skew(2^e) = 4 times Skew(2^{e-1}) minus 4 for e at least 4.
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Elements in $K_4$ and regulator maps of Fermat curves
Explicit non-trivial elements in K_4^{(3)} of Fermat curves are built uniformly in N, with regulators expressed via Zagier's trilogarithm and hypergeometric functions, plus numerical checks of Beilinson conjectures for N=3,4,6.
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Generalized quaternion NCI-groups, NNN-groups and NNND-groups
Q_{4n} is an NCI-group for all n≥2, never an NNN-group, and an NNND-group precisely when n is even and ≥6.
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Evaluating SageMath-Augmented LLM Agents for Computational and Experimental Mathematics
SageMath-augmented ReAct agents raise solve rates by +9.7 pp on average on a curated 133-problem RealMath subset, with GPT-5.5 reaching 75.2%.
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Computing canonical labellings of finite solvable groups
Defines a canonical labelling function for finite solvable groups via presentations and cohomology so that can(G) equals can(H) exactly when G and H are isomorphic.
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Stable quadratic polynomials over $\mathbb{Q}(i)$
Extends eventual stability of quadratic iterates f = x² + 1/c to Q(i) by proving the case c ≡ 2 mod 4 is stable, supporting a prior conjecture with an auxiliary check due to lack of ordering.
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Hyperelliptic Atkin-Lehner quotients of Shimura curves
Extends classifications of hyperelliptic Atkin-Lehner quotients from modular curves (D=1) and trivial quotients to general Shimura curves with coprime level.
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Analogues of Sylow's first theorem, Cauchy's theorem, and Hall's theorem for skew braces
Analogues of Sylow's first, Cauchy's, and Hall's theorems are established for finite skew braces, with application to classification of order pq examples.
-
Quadratic APN Functions in Dimension 8 via Gr\"obner Basis Search in a Self-Equivalence Subspace
Structured Groebner basis search in a 40-dimensional self-equivalence subspace of functions over F_{2^8} yields 566 quadratic APN functions in six classes, four of which are absent from prior databases of millions of instances.
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Orbits and incidence matrices for points, planes and lines regarding the twisted cubic in PG(3,q), q = 2, 3, 4
Classifies orbits of points, planes and lines under the stabilizer of the twisted cubic in PG(3,q) for q=2,3,4 and determines incidence matrices between the resulting orbit partitions.
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Distinguished defining polynomials for extensions of p-adic fields
An algorithm is provided for selecting distinguished defining polynomials for p-adic field extensions, serving as a key component in expanding the LMFDB p-adic fields database.
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Lower overhead fault-tolerant building blocks for noisy quantum computers
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
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On arc-transitive inner-automorphic Cayley graphs on dihedral groups
Authors classify arc-transitive inner-automorphic Cayley graphs on dihedral groups, supply a necessary condition plus infinite examples, and finish the 2-distance-transitive case.
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Groebner.jl: Fast Gr\"obner Tracing in Julia
A Julia F4 package with a reusable learn/apply tracing interface speeds up repeated Gröbner-basis computations, with 1.5–6.6x measured gains in solving and identifiability benchmarks.
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Improvements to Jacobian Arithmetic in Global Function Fields
Two optimizations to Jacobian arithmetic in global function fields—optimized reductions for typical cases and caching—yield faster practical performance with the first public software supporting unique divisor class representatives.