A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper proves that lattice point enumeration in moduli spaces satisfies topological recursion.
Bijective proof of map enumeration recursion formulae.
Paper proves 1-point recursions for various enumerative problems.
The topological recursion of Eynard and Orantin governs a variety of problems in enumerative geometry and mathematical physics. The recursion uses the data of a spectral curve to define an infinite family of multidifferentials. It has been conjectured that, under certain conditions, the spectral curve possesses a non-c…
We describe a method for recursively calculating Gromov-Witten invariants of all blowups of the projective plane. This recursive formula is different from the recursive formulas due to Göttsche and Pandharipande in the zero genus case, and Caporaso and Harris in the case of no blowups. We use tropical curves and a recu…
This paper reformulates double Hurwitz numbers using topological recursion.
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of t…
Study circular orders on groups, showing recursive enumerability and describing actions.
We introduce and study the Hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), which enumerates the number of linear chord diagrams of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are co…
Survey of methods for computing volumes of moduli spaces.
Classical Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. Monotone Hurwitz numbers restrict the enumeration by imposing a further monotonicity condition on such factorisations. In …
A typical census of 3-manifolds contains all manifolds (under various constraints) that can be triangulated with at most n tetrahedra. Al- though censuses are useful resources for mathematicians, constructing them is difficult: the best algorithms to date have not gone beyond n = 12. The underlying algorithms essential…
Consider a relatively hyperbolic group G. We prove that if G is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of G, a solution of its word problem, and generating sets of the parabolic subgroups. We also give an a…
We define and count lattice points in the moduli space of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli space. The enumeration produces polynomials with top degree coefficients tautological intersection numbers on the compactified moduli spac…
Researchers developed an algorithm to count all graph mosaics.
This research extends topological recursion to hyperbolic surfaces with tight boundaries and conical defects.
This research connects combinatorial Teichmüller space geometry to Weil-Petersson geometry.
STRIDE improves explainable AI by efficiently decomposing feature interactions without subset enumeration.
Criterion for stopping conjugacy class enumeration in triangle groups.
We announce a solution to several enumeration problems in topology of surfaces. This includes an enumeration of homotopy classes of sections of locally trivial fiber bundles over surfaces and a computation of non-abelian 1-cohomology of surfaces.
Enumerated all genus two handlebody-knots with seven crossings.
This paper improves robust cluster enumeration for RES data.
The article enumerates doubly symmetric diagrams for knots up to 18 crossings.
This is the third paper in a series devoted to enumerating the prime alternating knots and links. This paper establishes a method for enumerating the prime alternating links. It is shown that one may choose any prime alternating link diagram of a given minimal crossing size and by applications of just two operators (T …
PAG2ADMG algorithm enumerates all causal graphs consistent with a Markov equivalence class.
Constructive approach to Lie algebra gradings, computing maximal and enumerating all gradings.
Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded because they do not represent topological 3-manifolds. In this paper we show how …
This paper is a computation of the homotopy type of K, the space of long knots in R^3, the same space of knots studied by Vassiliev via singularity theory. Each component of K corresponds to an isotopy class of long knot, and we `enumerate' the components via the companionship trees associated to the knot. The knots wi…
Formula conjectured for rational cuspidal curves in projective plane.
A process enumerates rack elements from a presentation.
New algorithm enumerates decision tree Rashomon sets for continuous features.
The paper proposes an algorithm to enumerate K best models with distinct support vectors for SVM.
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial constraints, the only practical algorithms to date have been v…
New method estimates number of clusters robustly in noisy data.
New method finds 198,846 toric-colorable seeds of Picard number 5.
Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of these vertices, thus opening the way for substantial optimization. Here we give an…
A method to give users control over automated decisions by enumerating decision subspaces.
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings in terms of their generating functions. We show in particular how Fibonacci numb…
Let M be a compact, hyperbolizable 3-manifold with nonempty incompressible boundary and let AH(π_1(M)) denote the space of (conjugacy classes of) discrete faithful representations of π_1(M) into PSL 2 (C). The components of the interior MP(π_1(M)) of AH(π_1(M)) (as a subset of the appropriate representation variety) ar…
This paper deals with the enumeration of the higher order non-trivial compositions of the differential operations and the directional derivative in the space (). We present the recurrences for a counting the higher order non-trivial compositions.
The study enumerates virtual quandles up to isomorphism.
The study classifies semi-equivelar maps on Klein bottle.
The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible triangulation. In addition we present constraints upon the co…
A polynomial counts knot states for a specific type of knot.
Enumerated all principal congruence link complements in 3D space.
The paper addresses the -tangle enumeration problem. We introduce a notion of cascade diagram for -tangle projections. An effective enumeration algorithm for projections is proposed based on cascade representation. Tangles projections with up to 12 crossings are tabulated. We provide also pictures of alternating …
New method for counting distinct tilings with symmetrical surfaces.
We enumerate the small-volume manifolds that can be obtained by Dehn filling on Mom-2 and Mom-3 manifolds as defined by Gabai, Meyerhoff, and the author. In so doing we complete the proof that the Weeks manifold is the minimum-volume compact hyperbolic 3-manifold, as well as enumerating the 10 smallest one-cusped hyper…