A New Characterization of Prime Numbers and Alternations of Multisets
(2011) In Bachelor's Theses 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/student-papers/record/2517971
- author
- Logo, Selma
- supervisor
-
- Arne Meurman LU
- organization
- course
- MATX01 20111
- year
- 2011
- 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
- date added to LUP
- 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}},
}