CONTINUOUS QUANTITATIVE HELLY-TYPE RESULTS

被引：1
|
作者：
Fernandez Vidal, Tomas [1 ]
Galicer, Daniel [1 ]
Merzbacher, Mariano [1 ]
机构：
[1] Univ Buenos Aires, Dept Matemat, IMAS, Fac Cs Exactas & Nat,CONICET, Pab 1, RA-1428 Buenos Aires, DF, Argentina
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 05期
关键词：
Helly-type results; convex bodies; approximate John's decomposition; THEOREM;
D O I：
10.1090/proc/15844
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Brazitikos' results on quantitative Helly-type theorems (for the volume and for the diameter) rely on the work of Srivastava on sparsification of John's decompositions. We change this tool by a stronger recent result due to Friedland and Youssef which, together with an appropriate selection in the accuracy of the approximation, allows us to obtain Helly-type versions which are sensitive to the number of convex sets involved.
引用
下载
收藏
页码：2181 / 2193
页数：13
相关论文
共 50 条
  • [1] QUANTITATIVE HELLY-TYPE THEOREMS
    BARANY, I
    KATCHALSKI, M
    PACH, J
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 86 (01) : 109 - 114
  • [2] A QUANTITATIVE HELLY-TYPE THEOREM: CONTAINMENT IN A HOMOTHET
    Ivanov, Grigory
    Naszodi, Arton
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2022, 36 (02) : 951 - 957
  • [3] Discrete quantitative Helly-type theorems with boxes
    Dillon, Travis
    ADVANCES IN APPLIED MATHEMATICS, 2021, 129
  • [4] HELLY-TYPE PROBLEMS
    Barany, Imre
    Kalai, Gil
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 59 (04) : 471 - 502
  • [5] Quantitative Helly-Type Theorem for the Diameter of Convex Sets
    Brazitikos, Silouanos
    DISCRETE & COMPUTATIONAL GEOMETRY, 2017, 57 (02) : 494 - 505
  • [6] Quantitative Helly-Type Theorems via Sparse Approximation
    Almendra-Hernandez, Victor Hugo
    Ambrus, Gergely
    Kendall, Matthew
    DISCRETE & COMPUTATIONAL GEOMETRY, 2023, 70 (04) : 1707 - 1714
  • [7] Quantitative Helly-Type Theorem for the Diameter of Convex Sets
    Silouanos Brazitikos
    Discrete & Computational Geometry, 2017, 57 : 494 - 505
  • [8] Quantitative Helly-Type Theorems via Sparse Approximation
    Víctor Hugo Almendra-Hernández
    Gergely Ambrus
    Matthew Kendall
    Discrete & Computational Geometry, 2023, 70 : 1707 - 1714
  • [9] Quantitative Helly-type Theorems via Hypergraph Chains
    Jung, Attila
    ELECTRONIC JOURNAL OF COMBINATORICS, 2024, 31 (02):
  • [10] A HELLY-TYPE THEOREM FOR POLYGONS
    DERRY, D
    ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1966, 41 (05): : 290 - &
12345