# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### A New Characterization of Prime Numbers and Alternations of Multisets

(2011) In Bachelor's Theses in Mathematical Sciences MATX01 20111
Mathematics (Faculty of Sciences)
Abstract
This paper consists of two parts. In the first part the following problem is presented (see [1]): a king invites n couples for dinner at his round table with 2n+1 seats. For each couple there is an in advance prescribed distance between 1 and n at which the two spouses of the couple have to be seated from each other. We show that there is a solution to the king’s problem for every choice of distances between 1 and n if and only if the number of seats around the table, i.e. 2n + 1, is a prime number. In the second part we extend the following observation (see [3]): If two real multisets have different means then the multiset with the larger mean has an element larger than some element of the other multiset. We show that there exists a... (More)
This paper consists of two parts. In the first part the following problem is presented (see [1]): a king invites n couples for dinner at his round table with 2n+1 seats. For each couple there is an in advance prescribed distance between 1 and n at which the two spouses of the couple have to be seated from each other. We show that there is a solution to the king’s problem for every choice of distances between 1 and n if and only if the number of seats around the table, i.e. 2n + 1, is a prime number. In the second part we extend the following observation (see [3]): If two real multisets have different means then the multiset with the larger mean has an element larger than some element of the other multiset. We show that there exists a decreasing sequence of k + 1 elements that alternate between two multisets whose means as well as first k − 1 central moments agree. We also present an analoge to the result stated in terms of zeros of polynomials. (Less)
author
supervisor
organization
course
MATX01 20111
year
type
M2 - Bachelor Degree
subject
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUNFMA-4009-2011
ISSN
1654-6229
language
English
id
2517971
2014-12-15 14:19:14
date last changed
2018-10-11 16:22:09
```@misc{2517971,
abstract     = {This paper consists of two parts. In the first part the following problem is presented (see [1]): a king invites n couples for dinner at his round table with 2n+1 seats. For each couple there is an in advance prescribed distance between 1 and n at which the two spouses of the couple have to be seated from each other. We show that there is a solution to the king’s problem for every choice of distances between 1 and n if and only if the number of seats around the table, i.e. 2n + 1, is a prime number. In the second part we extend the following observation (see [3]): If two real multisets have different means then the multiset with the larger mean has an element larger than some element of the other multiset. We show that there exists a decreasing sequence of k + 1 elements that alternate between two multisets whose means as well as first k − 1 central moments agree. We also present an analoge to the result stated in terms of zeros of polynomials.},
author       = {Logo, Selma},
issn         = {1654-6229},
language     = {eng},
note         = {Student Paper},
series       = {Bachelor's Theses in Mathematical Sciences},
title        = {A New Characterization of Prime Numbers and Alternations of Multisets},
year         = {2011},
}

```