A New Characterization of Prime Numbers and Alternations of Multisets
(2011) In Bachelor's Thesis in Mathematical Sciences MATX01 20111Mathematics (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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/2517971
 author
 Logo, Selma
 supervisor

 Arne Meurman ^{LU}
 organization
 course
 MATX01 20111
 year
 2011
 type
 M2  Bachelor Degree
 subject
 publication/series
 Bachelor's Thesis in Mathematical Sciences
 report number
 LUNFMA40092011
 ISSN
 16546229
 language
 English
 id
 2517971
 date added to LUP
 20141215 14:19:14
 date last changed
 20150907 09:06:29
@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 = {16546229}, language = {eng}, note = {Student Paper}, series = {Bachelor's Thesis in Mathematical Sciences}, title = {A New Characterization of Prime Numbers and Alternations of Multisets}, year = {2011}, }