2006/05/19 by P. Jacob, Jacob, P., P. Mathieu +1
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CO #math.MP
paper · pdf · doi:10.48550/arxiv.math/0605551
arxiv created 2006/05/19 · arxiv updated 2009/12/01
A lattice-path description of K-restricted jagged partitions is presented. The corresponding lattice paths can have peaks only at even x coordinate and the maximal value of the height cannot be larger than K-1. Its weight is twice that of the corresponding jagged partitions. The equivalence is demonstrated at the level of generating functions. A bijection is given between K-restricted jagged partitions and partitions restricted by the following frequencies conditions: f2j-1 is even and fj+fj+1≤ K-1, where fj is the number of occurrences of the part j in the partition. Bijections are given between paths and these restricted partitions and between paths and partitions with successive ranks in a prescribed interval.