Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partitions into distinct parts without sequences, which are of particular interest due to their relationship with the Rogers-Ramanujan identities. Our main results include a double series representation for the generating function, an asymptotic formula for the enumeration function, and several combinatorial inequalities.
@article{10_37236_4970,
author = {Kathrin Bringmann and Karl Mahlburg and Karthik Nataraj},
title = {Distinct parts partitions without sequences},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {3},
doi = {10.37236/4970},
zbl = {1327.05023},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4970/}
}
TY - JOUR
AU - Kathrin Bringmann
AU - Karl Mahlburg
AU - Karthik Nataraj
TI - Distinct parts partitions without sequences
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/4970/
DO - 10.37236/4970
ID - 10_37236_4970
ER -
%0 Journal Article
%A Kathrin Bringmann
%A Karl Mahlburg
%A Karthik Nataraj
%T Distinct parts partitions without sequences
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/4970/
%R 10.37236/4970
%F 10_37236_4970
Kathrin Bringmann; Karl Mahlburg; Karthik Nataraj. Distinct parts partitions without sequences. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/4970
