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Algebraic and Geometric Topology, ISSN 1472-2747, 2019, Volume 19, Issue 3, pp. 1171 - 1206
In recent years the theory of dendroidal sets has emerged as an important framework for higher algebra... 
MATHEMATICS | NONCOMMUTATIVE SPECTRA | MODEL STRUCTURE | HOMOTOPY-THEORY | COMPLEXES
Journal Article
NEW YORK JOURNAL OF MATHEMATICS, ISSN 1076-9803, 2019, Volume 25, pp. 627 - 641
We show that the category of simplicial sets is a co-reflective subcategory of the category of cubical sets with connections, with the inclusion given by a version of the straightening functor... 
cubical sets | MATHEMATICS | model categories | simplicial sets | (infinity, 1)-categories
Journal Article
Computer Aided Geometric Design, ISSN 0167-8396, 05/2018, Volume 62, pp. 44 - 62
Simplicial sets and cubical sets are combinatorial structures which have been studied for a long time in Algebraic Topology... 
Bézier simploids | Simplicial sets | Cubical sets | Simploidal sets | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier simploids | Graphics software | Usage | Analysis
Journal Article
2015, Mathematical surveys and monographs, ISBN 9781470425456, Volume no. 209., viii, 218
Book
Journal of Algebra and its Applications, ISSN 0219-4988, 01/2019, Volume 18, Issue 1
Journal Article
Physical review letters, ISSN 1079-7114, 2010, Volume 104, Issue 18, p. 181301
Journal Article
1995, ISBN 9789810221379, xvi, 356
Book
Journal of Homotopy and Related Structures, ISSN 2193-8407, 12/2019, Volume 14, Issue 4, pp. 1043 - 1082
...}}$$ C -diagrams of simplicial sets, for a small index category $${\mathcal {C}}$$ C . When $${\mathcal {C}}$$ C is an EI-category satisfying some mild finiteness restrictions, we show that every fibration... 
Algebra | Functional Analysis | Fibre bundle | Simplicial space | Minimal fibration | Algebraic Topology | Mathematics | Number Theory | Diagram | MATHEMATICS
Journal Article
The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2012, Volume 42, Issue 2, pp. 353 - 423
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins... 
Morphisms | Equivalence relation | Homotopy theory | Maps | Axioms | Functors | Mathematics | Algebraic topology | Vertices | Topological spaces | Simplicial sets | Simplicial homotogy | MATHEMATICS | simplicial homotopy | 18G30 | 55U10
Journal Article
SIAM journal on numerical analysis, ISSN 1095-7170, 2017, Volume 55, Issue 1, pp. 131 - 143
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2019, Volume 11502, pp. 213 - 226
Conference Proceeding
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 06/2018, Volume 27, Issue 7, p. 1841013
In 2004, Carter, Elhamdadi and Saito defined a homology theory for set-theoretic Yang–Baxter operators... 
Homology | pre-cubical module | torsion | Yang-Baxter operators | pre-simplicial module | MATHEMATICS | KNOT INVARIANTS | ALGEBRAIC STRUCTURES | EQUATION
Journal Article
Constructive Approximation, ISSN 0176-4276, 4/2018, Volume 47, Issue 2, pp. 357 - 371
Sharp metric entropy estimates under Hausdorff distance are obtained for classes of bounded sets with positive reach, extending a well-known result... 
Star-shaped | 52A30 | Numerical Analysis | Analysis | Simplicial approximation | Mathematics | Hausdorff distance | Secondary 41A46 | Metric entropy | Primary 52C17 | Positive reach | MATHEMATICS | CONVEX-FUNCTIONS
Journal Article
Applied Categorical Structures, ISSN 0927-2852, 12/2016, Volume 24, Issue 6, pp. 765 - 796
The Catalan simplicial set ℂ is known to classify skew-monoidal categories in the sense that a map from ℂ... 
Geometry | Nerve | Skew monoidal | Category | Convex and Discrete Geometry | Simplicial set | Bicategory | Catalan | Monoidal | Mathematics | Theory of Computation | Mathematical Logic and Foundations | MATHEMATICS
Journal Article
Journal of Applied and Industrial Mathematics, ISSN 1990-4789, 1/2017, Volume 11, Issue 1, pp. 58 - 69
A graph is called a 1-triangle if, for its every maximal independent set I, every edge of this graph with both endvertices not belonging to I is contained exactly in one triangle with a vertex... 
edge-simplicial graph | perfect neighborhood set | triangle graph | NP-completeness | Mathematics, general | Mathematics | characterization | Studies | Set theory | Graph theory | Algorithms | Mathematical analysis | Triangles | Graphs | Mathematical models | Polynomials | Recognition
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 12/2012, Volume 19, Issue 4
The combinatorial Hopf algebra on building sets BSet extends the chromatic Hopf algebra of simple graphs... 
Building set | Graph | Cd-index | Simplicial complex | Hopf algebra | Symmetric function | Dehn- sommerville relations | MATHEMATICS | MATHEMATICS, APPLIED | Dehn-Sommerville relations | symmetric function | simplicial complex | POLYTOPES | INDEX | graph | cd-index | building set
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2016, Volume 302, pp. 869 - 1043
We compare two approaches to the homotopy theory of ∞-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets... 
Simplicial operads | Infinity-operads | Forest sets | Dendroidal sets | Quillen equivalence | Quillen model structures | MATHEMATICS | SETS | HOMOTOPY-THEORY | CATEGORIES
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2009, Volume 157, Issue 3, pp. 542 - 557
The combinatorial structure of simploidal sets generalizes both simplicial complexes and cubical complexes... 
Homology | Semi-simplicial sets | Simploidal sets | Topological based modeling | TOPOLOGY | MATHEMATICS, APPLIED | HOMOTOPY THEORY | Image processing | Analysis | Equipment and supplies | Modeling and Simulation | Computer Science
Journal Article
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