Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
EULER, THE SYMMETRIC GROUP AND THE RIEMANN ZETA FUNCTION
 

Summary: EULER, THE SYMMETRIC GROUP AND
THE RIEMANN ZETA FUNCTION
JEFFREY STOPPLE
1. INTRODUCTION
Let be a permutation in the symmetric group Sn. An ascent is an
occurrence of (j) < (j + 1) for 1 j n - 1. For example, the
permutation 24513 has 3 ascents. The Eulerian number n
k
is defined
to be the number of permutations in Sn with exactly k ascents. (The
Eulerian numbers are not to be confused with the Euler numbers
En.) Some of the elementary facts about them [2, chapter 6.2] are the
recursion
n
k
= (k + 1)
n - 1
k
+ (n - k)
n - 1

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics