Zobrazeno 1 - 10
of 15
pro vyhledávání: '"Viacheslav Grishukhin"'
This monograph identifies polytopes that are “combinatorially ℓ1-embeddable”, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform p
Autor:
Viacheslav Grishukhin
Publikováno v:
Moscow Journal of Combinatorics and Number Theory. 10:83-94
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1eb02ad71e7a1c0526521140fdcc976a
https://doi.org/10.2140/moscow.2021.10.83
https://doi.org/10.2140/moscow.2021.10.83
Autor:
Viacheslav Grishukhin
Publikováno v:
European Journal of Combinatorics. 80:151-156
There are two vectors related to a facet F of a parallelotope tiling. These are: facet vector l F of the lattice L of the tiling and normal vector p F of the facet F . The famous Voronoi conjecture is equivalent to the following assertion. There are
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::447c4be68cf237a515b875def632d3d3
https://doi.org/10.1016/j.ejc.2018.02.016
https://doi.org/10.1016/j.ejc.2018.02.016
Autor:
Michel Deza, Viacheslav Grishukhin
Publikováno v:
Mathematika. 51:1-10
Voronoi conjectured that any parallelotope is affinely equivalent to a Voronoi polytope. A parallelotope is defined by a set of m facet vectors pi and defines a set of m lattice vectors ti, 1 ≤ i ≤ m. We show that Voronoi’s conjecture is true f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::731d0c1592496d5fcbe453b1ea0a908a
https://doi.org/10.1112/s0025579300015461
https://doi.org/10.1112/s0025579300015461
Autor:
Michel Deza, Viacheslav Grishukhin
Publikováno v:
Geometriae Dedicata. 104:15-24
The nonrigidity degree of a lattice L, nrdL, is the dimension of the L-type domain to which L belongs. We complete here the table of nrd's of all irreducible root lattices and their duals (we give also the minimal rank of their Delaunay polytopes). I
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::216203e1161fc6f9f0922471b666a99d
https://doi.org/10.1023/b:geom.0000022863.32544.81
https://doi.org/10.1023/b:geom.0000022863.32544.81
Autor:
Robert Erdahl, Viacheslav Grishukhin
By a {\em Voronoi parallelotope} $P(a)$ we mean a parallelotope determined by a non-negative quadratic form $a$. It was studied by Voronoi in his famous memoir. For a set of vectors $\mathcal P$, we call its {\em dual} a set of vectors ${\mathcal P}^
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c425978669f5222481fdb35926c49cdc
Autor:
Michel Deza, Viacheslav Grishukhin
Publikováno v:
Journal of Statistical Planning and Inference. 95:175-195
Call bifaced any k-valent polyhedron, whose faces are pa a-gons and pb b-gons only, where 36 aib ,0 ip a ,0 6pb. We consider the case b62k=(k − 2) covering applications; so either k =3 6 aib 66, or (k; a; b; pa) = (4; 3; 4; 8). Call such a polyhedr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4eb00bcb14c5fb33391906bd6944fdbe
https://doi.org/10.1016/s0378-3758(00)00287-1
https://doi.org/10.1016/s0378-3758(00)00287-1
Autor:
Michel Deza, Viacheslav Grishukhin
Publikováno v:
Discrete Mathematics. :205-210
The edge-graphs of m -polygons and of 5 platonic solids admit (unique) isometric embedding into a half cube (of dimension m and 6, resp.). The skeletons of α n , β n , γ n are also l 1 -graphs but it was proved in Assouad (1991) that 24-cell and 6
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6ac3add633e902a6edb61354138f3829
https://doi.org/10.1016/s0012-365x(96)00169-0
https://doi.org/10.1016/s0012-365x(96)00169-0
Autor:
Michel Deza, Viacheslav Grishukhin
Publikováno v:
European Journal of Combinatorics. 17:143-156
The cut polytopePCutnis an L-polytope of the latticeLn,affinely generated by its vertices. We consider cut-sublattices ofLngenerated by subsets of cuts. Ifnis even,Lnis generated by an odd system. We give a description of sets of equiangular lines re
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::95f942fc382e0f8c4427828ef8c43b9b
https://doi.org/10.1006/eujc.1996.0013
https://doi.org/10.1006/eujc.1996.0013
Autor:
Viacheslav Grishukhin
Publikováno v:
European Journal of Combinatorics. 13:153-165
We give a complete description of the extreme rays of the comesMk of all metrics onk points fork ≤ 7. The coneM7 has more than 60 000 rays, and we use a computer program to make the computation. We give four collections of facets such that it is po
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2bc738d5a419324a496133f095ac9cdb
https://doi.org/10.1016/0195-6698(92)90021-q
https://doi.org/10.1016/0195-6698(92)90021-q