p-Ferrer diagram, p-linear ideals and arithmetical rank
Abstract
In this paper we introduce p-Ferrer diagram, note that 1- Ferrer diagram are the usual Ferrer diagrams or Ferrer board, and corresponds to planar partitions. To any p-Ferrer diagram we associate a p-Ferrer ideal. We prove that p-Ferrer ideal have Castelnuovo mumford regularity p+1. We also study Betti numbers, minimal resolutions of p-Ferrer ideals. Every p-Ferrer ideal is p-joined ideals in a sense defined in a fortcoming paper m2, which extends the notion of linearly joined ideals introduced and developped in the papers bm2, bm4,eghp and m1. We can observe the connection between the results on this paper about the Poincar\'e series of a p-Ferrer diagram and the rook problem, which consist to put k rooks in a non attacking position on the p-Ferrer diagram .
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