Steiner systems and configurations of points

被引：4

作者：

Ballico, Edoardo ^{[1
]}

Favacchio, Giuseppe ^{[2
]}

Guardo, Elena ^{[2
]}

Milazzo, Lorenzo ^{[2
]}

机构：

[1] Dipartimento Matemat, Via Sommar 14, I-38123 Povo, TN, Italy

[2] Dipartimento Matemat & Informat, Viale A Doria 6, I-95100 Catania, Italy

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2021年 / 89卷 / 02期

关键词：

Steiner systems; Monomial ideals; Symbolic powers; Stanley Reisner rings; Linear codes; UPPER CHROMATIC NUMBER; COHEN-MACAULAYNESS; QUADRUPLE SYSTEMS; STRICT COLORINGS; MINIMUM DISTANCE; TRIPLE; IDEALS; CODES; POWERS; SETS;

D O I：

10.1007/s10623-020-00815-x

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System S(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configuration of points and its Complement.

引用

下载

页码：199 / 219

页数：21

共 50 条

[41] On the location of Steiner points in uniformly-oriented Steiner trees
Nielsen, BK
Winter, P
Zachariasen, M
INFORMATION PROCESSING LETTERS, 2002, 83 (05) : 237 - 241
[42] The classification of Steiner triple systems on 27 points with 3-rank 24
Jungnickel, Dieter
Magliveras, Spyros S.
Tonchev, Vladimir D.
Wassermann, Alfred
DESIGNS CODES AND CRYPTOGRAPHY, 2019, 87 (04) : 831 - 839
[43] The classification of Steiner triple systems on 27 points with 3-rank 24
Dieter Jungnickel
Spyros S. Magliveras
Vladimir D. Tonchev
Alfred Wassermann
Designs, Codes and Cryptography, 2019, 87 : 831 - 839
[44] Steiner Points in the Space of Continuous Functions
Bednov, B. B.
MOSCOW UNIVERSITY MATHEMATICS BULLETIN, 2011, 66 (06) : 255 - 259
[45] On Indecomposable Polyhedra and The Number of Steiner Points
Goerigk, Nadja
Si, Hang
24TH INTERNATIONAL MESHING ROUNDTABLE, 2015, 124 : 343 - 355
[46] Configurations of points and strings
Reider, Igor
JOURNAL OF GEOMETRY AND PHYSICS, 2011, 61 (07) : 1158 - 1180
[47] CONFIGURATIONS OF CIRCLES AND POINTS
RIGBY, JF
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1983, 28 (AUG): : 131 - 148
[48] ANGLE SUMS AND STEINER POINTS OF POLYHEDRA
MANI, P
ISRAEL JOURNAL OF MATHEMATICS, 1971, 9 (03) : 380 - &
[49] The Steiner Problem for Infinitely Many Points
Paolini, E.
Ulivi, L.
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2010, 124 : 43 - 56
[50] Configurations of points and circles
de Vries, J
PROCEEDINGS OF THE KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, 1936, 39 (1/5): : 486 - 488

← 1 2 3 4 5 →