{"id":19,"date":"2012-09-05T11:22:25","date_gmt":"2012-09-05T15:22:25","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=19"},"modified":"2026-04-10T11:47:48","modified_gmt":"2026-04-10T15:47:48","slug":"publications","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/avince\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\n
\n

Publications<\/h1>\n\n\n\n

<\/p>\n\n\n\n

History<\/span><\/h3>\n\n\n\n

Mathematics in Uganda<\/a><\/p>\n\n\n\n

Fractal Geometry<\/span><\/h3>\n\n\n\n

Highly non-contractive iterated function systems on Euclidean space can have an attractor
Transition phenomena for the attractor of an iterated function system
Thresholds for One-Parameter Families of Affine Iterated Function Systems
Global Fractal Transformations and Global Addressing
Approximation of Rough Functions<\/a>
Old wine in fractal bottles I: orthogonal expansions on self-referential spaces via fractal transformations<\/a>
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems<\/a>
Developments in Fractal Geometry<\/a>
Fractal Continuation<\/a>
The Conley Attractors of an Iterated Function System<\/a>
Embedding the Symbolic Dynamics of Lorenz Maps<\/a>
The Entropy of a Special Overlapping Dynamical System<\/a>
Mobius Iterated Function Systems<\/a>
Fractal Homeomorphism for Bi-affine Iterated Function System<\/a>
The Eigenvalue Problem for Linear and Affine Iterated Function Systems<\/a>
Real Projective Iterated Function Systems<\/a>
The Chaos Game on a General Iterated Function System<\/a>
A Characterization of Hyperbolic Affine Iterated Function Systems<\/a><\/p>\n\n\n\n

Algebraic and Geometric Combinatorics<\/span><\/h3>\n\n\n\n

A combinatorial approach to binary positional number systems<\/a>
\nCritical itineraries of maps with constant slope and one discontinuity<\/a>
\nEnumeration of Viral Capsid Pathways: tree orbits under permutation group action<\/a>
\nOrthogonal Matroids<\/a>
\nAn Adjacency Criterion for Coxeter Matroids<\/a>
\nThe Lattice of Flats and its Underlying Flag Polytope<\/a>
\nA Geometric Characterization of Coxeter Matroids<\/a>
\nVariations on a Theorem of Ryser<\/a>
\nNon-Revisiting Paths on Surfaces with Low Genus<\/a>
\nNon-Revisiting Paths on Surfaces<\/a>
\nMap Duality and Generalizations <\/a>
\nThe Classification of Closed Surfaces Using Colored Graphs<\/a>
\nElementary Divisors of Graphs and Matroids<\/a>
\nA Shellable Poset that is not Lexicographically Shellable<\/a>
\nGraphic Matroids, Shellability and the Poincar\u00e9 Conjecture<\/a>
\nRegular Combinatorial Maps<\/a>
\nCombinatorial Maps<\/a>
\nPeriod of a Linear Recurrence<\/a><\/p>\n\n\n\n

Tiling<\/span><\/h3>\n\n\n\n

Self-Similar GIFS Tilings of Euclidean Space<\/a>
\nDistortion reversal in aperiodic tilings<\/a>
\nTilings from Graph Directed Iterated Function Systems<\/a>
\nSelf-Similar Polygonal Tiling<\/a>
\nFractal Tiling from an Iterated Function System<\/a>
\nA Property of Normal Tilings<\/a>
\nDigit Tiling of Euclidean Space<\/a>
\nThe Hausdorff Dimension of the Boundary of a Self-Similar Tile<\/a>
\nSelf-Replicating Tiles and their Boundary<\/a>
\nPeriodicity, Quasiperiodicity, and Bieberbach’s Theorem on Crystallographic Groups<\/a>
\nIsohedral Polyomino Tiling of the Plane<\/a>
\nReplicating Tessellations<\/a>
\nRep-Tiling Euclidean Space<\/a>
\nAn Isomorphism between the p-adic Integers and a Ring Associated with a Tiling<\/a><\/p>\n\n\n\n

Graph Theory<\/span><\/h3>\n\n\n\n

An extremal problem on a grid and an isoperimetric problem for polyominoes<\/a>
\nThe average order of a connected induced subgraph of a graph and union-intersection systems<\/a>
\nThe average size of a connected vertex set of a k-connected graph<\/a>
\nA Lower Bound on the Average Size of a Connected Vertex Set of a Graph<\/a>
\nThe Average Size of a Connected Vertex Set of a Graph – Explicit Formulas and Open Problems<\/a>
\nAparallel Digraphs and Splicing Machines<\/a>
\nCounting Connected Sets and Connected Partitions of a Graph<\/a>
\nThe Number of Ways to Assemble a Graph<\/a>
\nThe Average Order of a Subtree of a Tree<\/a>
\nInfinitely Many Trees have the Non-Sperner Subtree Property<\/a>
\nParity Versions of 2-Connectedness<\/a>
\nThe Integrity of a Cubic Graph<\/a>
\nMaps (in Handbook of Graph Theory)<\/a>
\nGraph Recurrence<\/a>
\nGeodesics in Graphs,
\nAn Extremal Set Problem, and Perfect Hash Families<\/a>
\nThe Separation Index of a Graph<\/a>
\nOn Representations of Some Thickness-Two Graphs<\/a>
\nCycles in a Graph of Lengths Differ by One or Two<\/a>
\nReconstruction of the Set of Branches of a Graph<\/a>
\nThe Spectral Radius of a Planar Graph<\/a>
\nDyck’s Map (3,7)_8 is a Counterexample to a Clique Covering Conjecture<\/a>
\nDiscrete Jordan Curve Theorems<\/a>
\nA New Counting Formula and its Application to Edge Reconstruction<\/a>
\nn-Graphs<\/a>
\nStar Chromatic Number<\/a>
\nThe Solution to an Extremal Problem on Balanced Extensions of Graphs<\/a>
\nStrongly Balanced Graphs and Random Graphs<\/a>
\nBalanced Extensions of Graphs and Hypergraphs<\/a>
\nLocally Homogeneous Graphs from Groups<\/a><\/p>\n\n\n\n

Discrete Geometry<\/span><\/h3>\n\n\n\n

Symmetry in Sphere-Based Assembly Configuration Spaces<\/a>
\nAn extremal problem and a grid and an isoperimetric problem for polyominoes<\/a>
\nArithmetic and Fourier Transform for the PYXIS Multi-Resolution Digital Earth Model<\/a>
\nComputing the Discrete Fourier Transform of a Hexagonal Lattice<\/a>
\nA Simplex Contained in a Sphere<\/a>
\nDiscrete Lines and Wandering Paths<\/a>
\nIndexing the Aperture 3 Hexagonal Discrete Global Grid<\/a>
\nIndexing a Discrete Global Grid<\/a>
\nA Rearrangement Inequality and the Permutahedron
\n<\/a><\/p>\n\n\n\n

Discrete Algorithms<\/span><\/h3>\n\n\n\n

A Framework for the Greedy Algorithm<\/a>
\nThe Greedy Algorithm and Coxeter Matroids<\/a>
\nScheduling Periodic Events<\/a><\/p>\n\n\n\n

Monthly Proplems<\/span><\/h3>\n\n\n\n

Almost Fixed Sets – Monthly Problem 10843<\/a>
\nSuper Regular Graphs – Monthly Problem 6617<\/a>
\nModular Power Series – Monthly Problem 10314<\/a>
\nScrambling Points on the Unit Circle – <\/a>Monthly Problem 6647<\/a><\/p>\n<\/div><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":289,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-19","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/users\/289"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":3035,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/19\/revisions\/3035"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}