Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Tristram Bogart"'
Publikováno v:
Discrete Analysis (2017)
Parametric Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior, Discrete Analysis 2017:4, 34 pp. Let $T$ be a triangle with vertices $(0,0)$, $(0,1/3)$, and $(1,0)$, and let $t$ be a positive integer. Then it is not hard to ch
Externí odkaz:
https://doaj.org/article/df9c2de9e2a141a5b12e4b679d9adcf1
Publikováno v:
Discrete & Computational Geometry. 67:462-491
A combinatorial polytope $P$ is said to be projectively unique if it has a single realization up to projective transformations. Projective uniqueness is a geometrically compelling property but is difficult to verify. In this paper, we merge two appro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::91dee16b47350cba063ab0adff94eccf
https://doi.org/10.1007/s00454-021-00347-8
https://doi.org/10.1007/s00454-021-00347-8
A natural operation on numerical semigroups is taking a quotient by a positive integer. If $\mathcal {S}$ is a quotient of a numerical semigroup with k generators, we call $\mathcal {S}$ a k-quotient. We give a necessary condition for a given numeric
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e2eaf9d3ba83a89c22ac37f2edcd9c23
http://arxiv.org/abs/2212.08285
http://arxiv.org/abs/2212.08285
Autor:
Tristram Bogart, Anna-Lena Horlemann-Trautmann, David Karpuk, Alessandro Neri, Mauricio Velasco
Publikováno v:
SIAM Journal on Discrete Mathematics. 35:2946-2970
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d428c9139a0d858609c5342dbc6d051e
https://doi.org/10.1137/20m1356658
https://doi.org/10.1137/20m1356658
Publikováno v:
SIAM Journal on Discrete Mathematics. 34:2363-2387
Given a parametric lattice with a basis given by polynomials in Z[t], we give an algorithm to construct an LLL-reduced basis whose elements are eventually quasi-polynomial in t: that is, they are given by formulas that are piecewise polynomial in t (
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd94468848b1cad4ed6d8df490f2f7a8
https://doi.org/10.1137/20m1327422
https://doi.org/10.1137/20m1327422
Autor:
Tristram Bogart, Kevin Woods
A wide variety of problems in combinatorics and discrete optimization depend on counting the set $S$ of integer points in a polytope, or in some more general object constructed via discrete geometry and first-order logic. We take a tour through numer
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ad96ba29915a23ee11e050a5c945c07a
http://arxiv.org/abs/2012.12976
http://arxiv.org/abs/2012.12976
Autor:
Edward D. Kim, Tristram Bogart
Publikováno v:
Combinatorica. 38:75-114
We construct a sequence of subset partition graphs satisfying the dimension reduction, adjacency, strong adjacency, and endpoint count properties whose diameter has a superlinear asymptotic lower bound. These abstractions of polytope graphs give furt
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16252afb6c88331be00829d3f2385c07
https://doi.org/10.1007/s00493-016-3327-8
https://doi.org/10.1007/s00493-016-3327-8
Let $f_1(n), \ldots, f_k(n)$ be polynomial functions of $n$. For fixed $n\in\mathbb{N}$, let $S_n\subseteq \mathbb{N}$ be the numerical semigroup generated by $f_1(n),\ldots,f_k(n)$. As $n$ varies, we show that many invariants of $S_n$ are eventually
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6986da676c1c1d0204441b0ab7a3db29
Publikováno v:
Research in Number Theory. 5
Two number fields are called arithmetically equivalent if they have the same Dedekind zeta function. In the 1970s Perlis showed that this is equivalent to the condition that for almost every rational prime $$\ell $$ the arithmetic type of $$\ell $$ i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16c3756d7ced1d71710714261de2a987
https://doi.org/10.1007/s40993-018-0139-5
https://doi.org/10.1007/s40993-018-0139-5
We consider an expansion of Presburger arithmetic which allows multiplication by $k$ parameters $t_1,\ldots,t_k$. A formula in this language defines a parametric set $S_\mathbf{t} \subseteq \mathbb{Z}^{d}$ as $\mathbf{t}$ varies in $\mathbb{Z}^k$, an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::55685e8bfe8557f53af137826b08b3ea