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- The algebraic combinatorial approach for Low-Rank Matrix Completion

few entries with tools from algebraic geometry and matroid theory The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework More specifically apart from introducing an algebraic combinatorial theory of low rank matrix completion we present probability one algorithms to decide whether a particular entry of the matrix can be completed We also describe methods to complete that entry from

Original URL path: http://theran.lt/papers/j010-matcomp.html (2016-04-26)

Open archived version from archive - Frameworks with forced symmetry II: orientation-preserving crystallographic groups

Louis Theran Journal Geometriae Dedicata 170 1 219 262 2014 Full text arXiv DOI We give a combinatorial characterization of minimally rigid planar frameworks with orientation preserving crystallographic symmetry under the constraint of forced symmetry The main theorems are proved by extending the methods of the first paper in this sequence from groups generated by a single rotation to groups generated by translations and rotations The proof makes use of

Original URL path: http://theran.lt/papers/j009-op.html (2016-04-26)

Open archived version from archive - Generic combinatorial rigidity of periodic frameworks

Louis Theran Journal Advances in Mathematics 233 1 291 331 2013 Full text arXiv DOI We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks The characterization is a true analogue of the Maxwell Laman Theorem from rigidity theory it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorithms To prove our rigidity theorem we introduce and

Original URL path: http://theran.lt/papers/j008-periodic.html (2016-04-26)

Open archived version from archive - Topological designs

221 233 2013 Full text arXiv DOI Benson Farb and Chris Leininger had asked how many pairwise non isotopic simple closed curves can be placed on a surface of genus in such a way that any two of the curves intersect at most once In this note we use combinatorial methods to give bounds a lower bound of curves and an exponential upper bound While the bounds for the general

Original URL path: http://theran.lt/papers/j007-farbtown.html (2016-04-26)

Open archived version from archive - Natural realizations of sparsity matroids

Journal Ars Mathematica Contemporanea 4 1 2011 Full text arXiv A hypergraph with vertices and hyperedges with endpoints each is sparse if for all sub hypergraphs on vertices and edges For integers and satisfying this is known to be a linearly representable matroidal family Motivated by problems in rigidity theory we give a new linear representation theorem for the sparse hypergraphs that is natural i e the representing matrix captures

Original URL path: http://theran.lt/papers/j006-natural.html (2016-04-26)

Open archived version from archive - Slider-pinning rigidity: a Maxwell–Laman-type theorem

Authors Ileana Streinu and Louis Theran Journal Discrete Computational Geometry 44 4 812 837 2010 Full text arXiv DOI We define and study slider pinning rigidity giving a complete combinatorial characterization This is done via direction slider networks which are

Original URL path: http://theran.lt/papers/j005-sliders.html (2016-04-26)

Open archived version from archive - Sparse hypergraphs and pebble game algorithms

arXiv DOI A hypergraph is sparse if no subset spans more than hyperedges We characterize sparse hypergraphs in terms of graph theoretic matroidal and algorithmic properties We extend several well known theorems of Haas Lovász Nash Williams Tutte and White and Whiteley linking arboricity of graphs to certain counts on the number of edges We also address the problem of finding lower dimensional representations of sparse hypergraphs and identify a

Original URL path: http://theran.lt/papers/j004-hypergraphs.html (2016-04-26)

Open archived version from archive - Sparsity-certifying graph decompositions

characterization of the family of k ℓ sparse graphs and algorithmic solutions to a family of problems concerning tree decompositions of graphs Special instances of sparse graphs appear in rigidity theory and have received increased attention in recent years In particular our colored pebbles generalize and strengthen the previous results of Lee and Streinu and give a new proof of the Tutte Nash Williams characterization of arboricity We also present

Original URL path: http://theran.lt/papers/j003-coloredpg.html (2016-04-26)

Open archived version from archive