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pro vyhledávání: '"Sabalka, Lucas"'
Autor:
Sabalka, Lucas Adam.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.
Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3839. Adviser: Ilya Kapovich. Includes bibliographical references (leaves 101-103) Available on micr
Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3839. Adviser: Ilya Kapovich. Includes bibliographical references (leaves 101-103) Available on micr
The space of configurations of n ordered points in the plane serves as a classifying space for the pure braid group PB_n. Elements of Thompson's group F admit a model similar to braids, except instead of braiding the strands split and merge. In Belk'
Externí odkaz:
http://arxiv.org/abs/1306.6534
Autor:
Sabalka, Lucas, Savchuk, Dmytro
One of the most useful tools for studying the geometry of the mapping class group has been the subsurface projections of Masur and Minsky. Here we propose an analogue for the study of the geometry of Out(F_n) called submanifold projection. We use the
Externí odkaz:
http://arxiv.org/abs/1211.3111
Autor:
Sabalka, Lucas, Savchuk, Dmytro
Let G be a finitely generated free, free abelian of arbitrary exponent, free nilpotent, or free solvable group, or a free group in the variety A_mA_n, and let A = {a_1,..., a_r} be a basis for G. We prove that, in most cases, if S is a subset of a ba
Externí odkaz:
http://arxiv.org/abs/1103.2992
Autor:
Sabalka, Lucas, Savchuk, Dmytro
The group $\Out$ of outer automorphisms of the free group has been an object of active study for many years, yet its geometry is not well understood. Recently, effort has been focused on finding a hyperbolic complex on which $\Out$ acts, in analogy w
Externí odkaz:
http://arxiv.org/abs/1007.1998
Brenti and Welker have shown that for any simplicial complex X, the face vectors of successive barycentric subdivisions of X have roots which converge to fixed values depending only on the dimension of X. We improve and generalize this result here. W
Externí odkaz:
http://arxiv.org/abs/1002.3201
Autor:
Farley, Daniel, Sabalka, Lucas
Let G be a graph. The (unlabeled) configuration space of n points on G is the space of all n-element subsets of G. The fundamental group of such a configuration space is called a graph braid group. We use a version of discrete Morse theory to compute
Externí odkaz:
http://arxiv.org/abs/0907.2730
Autor:
Kramer, Joshua Brown, Sabalka, Lucas
Publikováno v:
International Journal of Computational Geometry and Applications, 20(6):653-684, 2010
We consider three related problems of robot movement in arbitrary dimensions: coverage, search, and navigation. For each problem, a spherical robot is asked to accomplish a motion-related task in an unknown environment whose geometry is learned by th
Externí odkaz:
http://arxiv.org/abs/0903.4696
Autor:
Kramer, Josh Brown, Sabalka, Lucas
Publikováno v:
Journal of Combinatorial Theory, Series A, 117(8): 1136-1142, 2010
Let $F$ be a finite field. A multiset $S$ of integers is projection-forcing if for every linear function $\phi : F^n \to F^m$ whose multiset of weight changes is $S$, $\phi$ is a coordinate projection up to permutation and scaling of entries. The Mac
Externí odkaz:
http://arxiv.org/abs/0903.4237
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