Mohan

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20242026

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6 papers · 1 filter

math.NT2024

On additive complements in the complement of a set of natural numbers

Bhuwanesh Rao Patil, Mohan

Let $A$ be a set of natural numbers. A set $B$ , a set of natural numbers, is an additive complement of the set $A$ if all sufficiently large natural numbers can be represented in t…

math.NT2024

Some direct and inverse problems for the Restricted Signed sumset in set of integers

Mohan, Raj Kumar Mistri, Ram Krishna Pandey

Given a positive integer $h$ and a nonempty finite set of integers $A = {a_{1}, a_{2}, \dots, a_{k}}$ , the restricted $h$ -fold signed sumset of $A$ , denoted by $h_{\pm}^{\land} A$ , i…

math.NT2024

Freiman's $(3 k - 4)$ -like results for subset and subsequence sums

Mohan, Jagannath Bhanja, Ram Krishna Pandey

For a nonempty finite set $A$ of integers, let $S (A) = {\sum_{b \in B} b : \emptyset \neq = B \subseteq A}$ be the set of all nonempty subset sums of $A$ . In 1995, Nathan…

math.NT2024

On additive complement with special structures

Mohan, Bhuwanesh Rao Patil, Ram Krishna Pandey

Let $A$ be a set of natural numbers. A set $B$ , a set of natural numbers, is said to be an additive complement of the set $A$ if all sufficiently large natural numbers can be repre…

math.NT2024

Generalized H-fold sumset and Subsequence sum

Mohan, Ram Krishna Pandey

Let $A$ and $H$ be nonempty finite sets of integers and positive integers, respectively. The generalized $H$ -fold sumset, denoted by $H^{(r)} A$ , is the union of the sumsets $h^{(r)…

math.NT2024

Extended inverse theorems for $h$ -fold sumsets in integers

Mohan, Ram Krishna Pandey

Let $h \geq 2$ , $k \geq 5$ 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 < \left|hA\right…

On additive complements in the complement of a set of natural numbers

Some direct and inverse problems for the Restricted Signed sumset in set of integers

Freiman's (3k−4)-like results for subset and subsequence sums

On additive complement with special structures

Generalized H-fold sumset and Subsequence sum

Extended inverse theorems for h-fold sumsets in integers

Freiman's $(3 k - 4)$ -like results for subset and subsequence sums

Extended inverse theorems for $h$ -fold sumsets in integers