2006/08/31 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/0609001
12 pages; minor corrections, version to appear in Discrete Math
arxiv created 2008/01/15 · arxiv updated 2009/12/01
A bijection is presented between (1): partitions with conditions fj+fj+1≤ k-1 and f1≤ i-1, where fj is the frequency of the part j in the partition, and (2): sets of k-1 ordered partitions (n(1), n(2), ..., n(k-1)) such that n(j)_ℓ ≥ n(j)ℓ+1 + 2j and n(j)mj ≥ j+ \rm max (j-i+1,0)+ 2j (mj+1+... + mk-1), where mj is the number of parts in n(j). This bijection entails an elementary and constructive proof of the Andrews multiple-sum enumerating partitions with frequency conditions. A very natural relation between the k-1 ordered partitions and restricted paths is also presented, which reveals our bijection to be a modification of Bressoud's version of the Burge correspondence.