EXTENDED INVERSE THEOREMS FOR h-FOLD SUMSETS IN INTEGERS

被引：0

作者：

Mohan ^{[1
]}

Pandey, Ram Krishna ^{[1
]}

机构：

[1] Indian Inst Technol Roorkee, Dept Math, Roorkee 247667, Uttarakhand, India

来源：

CONTRIBUTIONS TO DISCRETE MATHEMATICS | 2023年 / 18卷 / 02期

关键词：

Sumset; h-fold sumset; inverse problem; extended inverse problem;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let h >= 2, k >= 5 be integers and A be a nonempty finite set of k integers. Very recently, Tang and Xing studied extended inverse theorems for hk - h + 1 < |hA| < hk + 2h - 3. In this paper, we extend the work of Tang and Xing and study all possible inverse theorems for hk - h + 1 <= |hA| < hk + 2h + 1. Furthermore, we give a range of |hA| for which inverse problems are not possible.

引用

页码：129 / 145

页数：17

共 14 条

[1] On the structure of the h-fold sumsets
Zhou, Jun-Yu
Yang, Quan-Hui
COMPTES RENDUS MATHEMATIQUE, 2021, 359 (04) : 493 - 500
[2] On the cardinality of general h-fold sumsets
Yang, Quan-Hui
Chen, Yong-Gao
EUROPEAN JOURNAL OF COMBINATORICS, 2015, 47 : 103 - 114
[3] Direct and inverse theorems on signed sumsets of integers
Bhanja, Jagannath
Pandey, Ram Krishna
JOURNAL OF NUMBER THEORY, 2019, 196 : 340 - 352
[4] EXTENDED INVERSE THEOREMS FOR RESTRICTED SUMSET IN INTEGERS
Mohan
Pandey, Ram krishna
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2024, 61 (05) : 1339 - 1367
[5] DIRECT AND INVERSE PROBLEMS FOR RESTRICTED SIGNED SUMSETS IN INTEGERS
Bhanja, Jagannath
Komatsu, Takao
Pandey, Ram Krishna
CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2021, 16 (01) : 28 - 46
[6] GENERALIZED H-FOLD SUMSET AND SUBSEQUENCE SUM
Mohan
Pandey, Ram Krishna
arXiv, 1600,
[7] Few products, many h-fold sums
Bush, Albert
Croot, Ernie
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (08) : 2107 - 2128
[8] Generalized H-fold sumset and Subsequence sum
Mohan
Pandey, Ram Krishna
COMPTES RENDUS MATHEMATIQUE, 2024, 362 : 1 - 19
[9] h-FOLD SUMS FROM A SET WITH FEW PRODUCTS
Croot, Ernie
Hart, Derrick
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2010, 24 (02) : 505 - 519
[10] h-fold Symmetric quasicrystallography from affine Coxeter groups
Koca, N. O.
Koca, M.
Al-Shidhani, S.
XXII INTERNATIONAL CONFERENCE ON INTEGRABLE SYSTEMS AND QUANTUM SYMMETRIES (ISQS-22), 2014, 563

← 1 2 →