Zobrazeno 1 - 10
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pro vyhledávání: '"LUTZ, BOB"'
Autor:
Lutz, Bob
This paper studies graphical analogs of symmetric products and unordered configuration spaces in topology. We do so from the perspective of the discrete homotopy theory introduced by Barcelo et al. Our first result is a combinatorial version of a the
Externí odkaz:
http://arxiv.org/abs/2005.13557
Autor:
Lutz, Bob
This paper studies a discrete homotopy theory for graphs introduced by Barcelo et al. We prove two main results. First we show that if $G$ is a graph containing no 3- or 4-cycles, then the $n$th discrete homotopy group $A_n(G)$ is trivial for all $n\
Externí odkaz:
http://arxiv.org/abs/2003.02390
Autor:
Lutz, Bob
We prove that the cone over a Dirichlet arrangement is supersolvable if and only if its Orlik-Solomon algebra is Koszul. This was previously shown for four other classes of arrangements. We exhibit an infinite family of cones over Dirichlet arrangeme
Externí odkaz:
http://arxiv.org/abs/1810.03518
Autor:
Lutz, Bob
Publikováno v:
Adv. Appl. Math., vol. 137 (2022)
This paper introduces Dirichlet matroids, a generalization of graphic matroids arising from electrical networks. We present four main theorems. First, we exhibit a matroid quotient involving geometric duals of networks embedded in surfaces with bound
Externí odkaz:
http://arxiv.org/abs/1809.10100
Autor:
Lutz, Bob
This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize descriptions of combinatorial features of graphic arrangements
Externí odkaz:
http://arxiv.org/abs/1709.01227
Autor:
Lutz, Bob
Recent work has introduced the study of graphical properties of cyclic supercharacters, functions $\mathbb{Z}/n\mathbb{Z}\to \mathbb{C}$ whose values are exponential sums with close connections to Gauss sums and Gaussian periods. Plots of these funct
Externí odkaz:
http://arxiv.org/abs/1601.01031
Publikováno v:
Notices Amer. Math. Soc. 62 (2015), no.8, 878-888
Gaussian periods, when viewed appropriately, exhibit a dazzling and eclectic host of visual qualities. This brief survey reviews the historical context and summarizes our current knowledge of graphical properties of Gaussian periods.
Comment: 16
Comment: 16
Externí odkaz:
http://arxiv.org/abs/1501.07507
Autor:
LUTZ, BOB, Hersh, Patricia
Publikováno v:
Proceedings of the American Mathematical Society, 2019 Nov 01. 147(11), 4937-4947.
Externí odkaz:
https://www.jstor.org/stable/26801617
Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the Monthly, despite its intense coverage of quotient sets over the years.
Comment: 9 pages, to appear in the Americ
Comment: 9 pages, to appear in the Americ
Externí odkaz:
http://arxiv.org/abs/1312.1036