On partitions without small parts

J.-L. Nicolas; A. Sárközy

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 1, page 227-254
  • ISSN: 1246-7405

Abstract

top
Let r ( n , m ) denote the number of partitions of n into parts, each of which is at least m . By applying the saddle point method to the generating series, an asymptotic estimate is given for r ( n , m ) , which holds for n → ∞ , and 1 ≤ m ≤ c 1 n log n c 2 .

How to cite

top

Nicolas, J.-L., and Sárközy, A.. "On partitions without small parts." Journal de théorie des nombres de Bordeaux 12.1 (2000): 227-254. <http://eudml.org/doc/248515>.

@article{Nicolas2000,
abstract = {Let $r(n, m)$ denote the number of partitions of $n$ into parts, each of which is at least $m$. By applying the saddle point method to the generating series, an asymptotic estimate is given for $r (n, m)$, which holds for $n \rightarrow \infty $, and $1 \le m \le c_1 \dfrac\{n\}\{\left(\log \,n\right)^\{c_2\}\}$.},
author = {Nicolas, J.-L., Sárközy, A.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {saddle point method; generating function; partition function; asymptotic estimate},
language = {eng},
number = {1},
pages = {227-254},
publisher = {Université Bordeaux I},
title = {On partitions without small parts},
url = {http://eudml.org/doc/248515},
volume = {12},
year = {2000},
}

TY - JOUR
AU - Nicolas, J.-L.
AU - Sárközy, A.
TI - On partitions without small parts
JO - Journal de théorie des nombres de Bordeaux
PY - 2000
PB - Université Bordeaux I
VL - 12
IS - 1
SP - 227
EP - 254
AB - Let $r(n, m)$ denote the number of partitions of $n$ into parts, each of which is at least $m$. By applying the saddle point method to the generating series, an asymptotic estimate is given for $r (n, m)$, which holds for $n \rightarrow \infty $, and $1 \le m \le c_1 \dfrac{n}{\left(\log \,n\right)^{c_2}}$.
LA - eng
KW - saddle point method; generating function; partition function; asymptotic estimate
UR - http://eudml.org/doc/248515
ER -

References

top
  1. [1] J. Dixmier, J.-L. Nicolas, Partitions without small parts. Number theory, Vol. I (Budapest, 1987), 9-33, Colloq. Math. Soc. János Bolyai51, North-Holland, Amsterdam, 1990. Zbl0707.11072MR1058207
  2. [2] J. Dixmier, J.-L. Nicolas, Partitions sans petits sommants. A tribute to Paul Erdõs, 121-152, Cambridge Univ. Press, Cambridge, 1990. Zbl0719.11067MR1117009
  3. [3] P. Erdõs, J.-L. Nicolas, M. Szalay, Partitions into parts which are unequal and large. Number theory (Ulm, 1987), 19-30, Lecture Notes in Math., 1380, Springer, New York-Berlin, 1989. Zbl0679.10013MR1009791
  4. [4] P. Erdõs, M. Szalay, On the statistical theory of partitions. Topics in classical number theory, Vol. I, II (Budapest, 1981), 397-450, Colloq. Math. Soc. János Bolyai34, North-Holland, Amsterdam-New York, 1984. Zbl0548.10010MR781149
  5. [5] G. Freiman, J. Pitman, Partitions into distinct large parts. J. Australian Math. Soc. Ser.A57 (1994), 386-416. Zbl0824.11064MR1297011
  6. [6] G. Szekeres, An asymptotic formula in the theory of partitions. Quart. J. Math. Oxford2 (1951), 85-108. Zbl0042.04102MR43129
  7. [7] G. Szekeres, Some asymptotic formulae in the theory of partitions II. Quart. J. Math. Oxford4 (1953), 96-111. Zbl0050.04101MR57279

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.