EUDML

Let $h, k$ be fixed positive integers, and let $A$ be any set of positive integers. Let $h A : = {a_{1} + a_{2} + \dots + a_{r} : a_{i} \in A, r \leq h}$ denote the set of all integers representable as a sum of no more than $h$ elements of $A$ , and let $n (h, A)$ denote the largest integer $n$ such that ${1, 2, ..., n} \subseteq h A$ . Let $n (h, k) : = {max}_{A} : n (h, A)$ , where the maximum is taken over all sets $A$ with $k$ elements. We determine $n (h, A)$ when the elements of $A$ are in geometric progression. In particular, this results in the evaluation of $n (h, 2)$ and yields surprisingly sharp lower bounds for $n (h, k)$ , particularly for $k = 3$ .

Density of M-sets in arithmetic progression

Soma Gupta; Amitabha Tripathi — 1999

Acta Arithmetica

Graphic sequences of trees and a problem of Frobenius

Gautam Gupta; Puneet Joshi; Amitabha Tripathi — 2007

Czechoslovak Mathematical Journal

We give a necessary and sufficient condition for the existence of a tree of order $n$ with a given degree set. We relate this to a well-known linear Diophantine problem of Frobenius.

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A note on the postage stamp problem.

On a linear Diophantine problem of Frobenius.

On the Frobenius problem for ${a^{k}, a^{k} + 1, a^{k} + a, \dots, a^{k} + a^{k - 1}}$ .

On a variation of the coin exchange problem for arithmetic progressions.

On the Frobenius problem for geometric sequences.

On a generalization of the coin exchange problem for three variables.

A comparison of dispersion and Markov constants

The postage stamp problem and arithmetic in base $r$

Density of M-sets in arithmetic progression

Graphic sequences of trees and a problem of Frobenius