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Start Over Creator Tripathi, Amitabha

1. Graphic sequences of trees and a problem of Frobenius

Creator:
Gupta, Gautam, Joshi, Puneet, and Tripathi, Amitabha
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
graphic and tree-graphic
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The postage stamp problem and arithmetic in base $r$

Creator:
Tripathi, Amitabha
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$h$-basis, extremal $h$-basis, and geometric progression
Language:
English
Description:
Let $h,k$ be fixed positive integers, and let $A$ be any set of positive integers. Let $hA:=\{a_1+a_2+\cdots +a_r\colon a_i \in A, r \le h\}$ 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 $\{1,2,\ldots ,n\} \subseteq hA$. Let $n(h,k):=\max _A\colon n(h,A)$, 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 $k=3$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public