Zobrazeno 1 - 10 of 52 pro vyhledávání: '"Christine Bachoc"'
1
Revisiting Kneser’s Theorem for Field Extensions
Autor: Gilles Zémor, Christine Bachoc, Oriol Serra
Publikováno v: Combinatorica
Combinatorica, Springer Verlag, 2018, 38 (4), pp.759-777
Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
A Theorem of Hou, Leung and Xiang generalised Kneser's addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an altern
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a6092aae023863e31b393aeb69987d9f
https://hal.archives-ouvertes.fr/hal-01951358
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2
Towards a function field version of Freiman's Theorem
Autor: Gilles Zémor, Alain Couvreur, Christine Bachoc
Publikováno v: Algebraic Combinatorics
Algebraic Combinatorics, 2018, 1 (4), pp.501-521. ⟨10.5802/alco.19⟩
Algebraic Combinatorics, MathOA, 2018, 1 (4), pp.501-521. ⟨10.5802/alco.19⟩
We discuss a multiplicative counterpart of Freiman's $3k-4$ theorem in the context of a function field $F$ over an algebraically closed field $K$. Such a theorem would give a precise description of subspaces $S$, such that the space $S^2$ spanned by
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https://hal.science/hal-01584034
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3
An analogue of Vosper's theorem for extension fields
Autor: Gilles Zémor, Oriol Serra, Christine Bachoc
Publikováno v: Math. Proc. Cambridge Phil. Soc.
Math. Proc. Cambridge Phil. Soc., 2017, ⟨10.1017/S0305004117000044⟩
Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
We are interested in characterising pairs $S,T$ of $F$-linear subspaces in a field extension $L/F$ such that the linear span $ST$ of the set of products of elements of $S$ and of elements of $T$ has small dimension. Our central result is a linear ana
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https://hdl.handle.net/2117/115387
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4
On the density of sets avoiding parallelohedron distance 1
Autor: Arnaud Pêcher, Philippe Moustrou, Christine Bachoc, Thomas Bellitto
Publikováno v: Bachoc, C, Bellitto, T, Moustrou, P & Pêcher, A 2019, ' On the Density of Sets Avoiding Parallelohedron Distance 1 ', Discrete & Computational Geometry, vol. 62, no. 3, pp. 497-524 . https://doi.org/10.1007/s00454-019-00113-x
Discrete and Computational Geometry
Discrete and Computational Geometry, 2019, 62 (3), pp.497-524. ⟨10.1007/s00454-019-00113-x⟩
Discrete and Computational Geometry, Springer Verlag, 2019, 62 (3), pp.497-524. ⟨10.1007/s00454-019-00113-x⟩
The maximal density of a measurable subset of $${{\mathbb {R}}}^n$$ avoiding Euclidean distance 1 is unknown except in the trivial case of dimension 1. In this paper, we consider the case of a distance associated to a polytope that tiles space, where
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5
The Theta Number of Simplicial Complexes
Autor: Anna Gundert, Alberto Passuello, Christine Bachoc
We introduce a generalization of the celebrated Lov\'asz theta number of a graph to simplicial complexes of arbitrary dimension. Our generalization takes advantage of real simplicial cohomology theory, in particular combinatorial Laplacians, and prov
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7
Optimality and uniqueness of the (4,10,1/6) spherical code
Autor: Frank Vallentin, Christine Bachoc
Publikováno v: Journal of Combinatorial Theory, Series A. 116:195-204
Linear programming bounds provide an elegant method to prove optimality and uniqueness of an (n,N,t) spherical code. However, this method does not apply to the parameters (4,10,1/6). We use semidefinite programming bounds instead to show that the Pet
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::18d0ccaa6cb4452d43f990d3b0fcec9b
https://doi.org/10.1016/j.jcta.2008.05.001
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8
The density of sets avoiding distance 1 in Euclidean space
Autor: Alberto Passuello, Alain Thiery, Christine Bachoc
We improve by an exponential factor the best known asymptotic upper bound for the density of sets avoiding 1 in Euclidean space. This result is obtained by a combination of an analytic bound that is an analogue of Lovasz theta number and of a combina
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https://hal.archives-ouvertes.fr/hal-00935665v2/document
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9
On theta series vanishing at ∞ and related lattices
Autor: Christine Bachoc, Riccardo Salvati Manni
Publikováno v: Acta Arithmetica. 124:59-71
We consider theta series with the highest possible order of vanishing at infinity when the level is a power of 2 or 3 and the lattices associated to these theta series. We prove that these lattices are constructed from binary, respectively ternary co
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https://doi.org/10.4064/aa124-1-5
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10
Codes and designs in Grassmannian spaces
Autor: Christine Bachoc, Renaud Coulangeon, Eiichi Bannai
Publikováno v: Discrete Mathematics. 277:15-28
The notion of t-design in a Grassmannian space G"m","n was introduced by the first and last authors and G. Nebe in a previous paper. In the present work, we give a general lower bound for the size of such designs. The method is inspired by Delsarte,
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https://doi.org/10.1016/s0012-365x(03)00151-1
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