Multiple partitions, lattice paths and a Burge-Bressoud-type correspondence

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dc.creatorJacob, P
dc.creatorMathieu, P.
dc.date2006-08-31
dc.date2008-01-15
dc.date.accessioned2026-07-07T08:54:25Z
dc.date.available2026-07-07T08:54:25Z
dc.descriptionA bijection is presented between (1): partitions with conditions $f_j+f_{j+1}\leq k-1$ and $ f_1\leq i-1$, where $f_j$ 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 $n^{(j)}_\ell \geq n^{(j)}_{\ell+1} + 2j$ and $ n^{(j)}_{m_j} \geq j+ {\rm max} (j-i+1,0)+ 2j (m_{j+1}+... + m_{k-1})$, where $m_j$ 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.
dc.description12 pages; minor corrections, version to appear in Discrete Math
dc.identifierhttps://arxiv.org/abs/math/0609001
dc.identifierhttp://arxiv.org/abs/math/0609001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145923
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.titleMultiple partitions, lattice paths and a Burge-Bressoud-type correspondence
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