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- W1639103811 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 cite{m2}, which extends the notion of linearly joined ideals introduced and developped in the papers cite{bm2}, cite{bm4},cite{eghp} and cite{m1}. We can observe the connection between the results on this paper about the Poincare series of a $p-$Ferrer diagram $Phi $and the rook problem, which consist to put $k$ rooks in a non attacking position on the $p-$Ferrer diagram $Phi $." @default.
- W1639103811 created "2016-06-24" @default.
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- W1639103811 date "2008-11-20" @default.
- W1639103811 modified "2023-09-27" @default.
- W1639103811 title "$p-$Ferrer diagram, $p-$linear ideals and arithmetical rank" @default.
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