Paper Info
Title
The proof of a conjecture of Simion for certain partitions
Abstract
Simion has a conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. The conjecture concerns the unimodality of a sequence of these numbers where the sum of the length and width of each rectangle is a constant and where the partition is constant. This paper demonstrates this unimodality if the partition is self-conjugate or if the Ferrers diagram of the partition has precisely one column or one row. This paper also shows log concavity for partitions of “staircase” shape via a Reflection Principle argument.
Year
DOI
Venue
2000
10.1016/S0012-365X(00)00111-4
Discrete Mathematics
Keywords
Field
DocType
partitions,lattice paths,certain partition,unimodality,reflection principle
Discrete mathematics,Unimodality,Combinatorics,Lattice (order),Rectangle,Diagram,Partition (number theory),Conjecture,Grid,Mathematics,Reflection principle
Journal
Volume
Issue
ISSN
224
1-3
Discrete Mathematics
Citations 
PageRank 
References 
1
0.51
0
Authors
1
Name
Order
Citations
PageRank
Martin Hildebrand110.51