Results 1 to 10 of about 2,246 (93)
Patterns in matchings and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Extending the notion of pattern avoidance in permutations, we study matchings and set partitions whose arc diagram representation avoids a given configuration of three arcs.
Jonathan Bloom, Sergi Elizalde
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Two Vignettes On Full Rook Placements [PDF]
Australas. J Comb., 2013 Using bijections between pattern-avoiding permutations and certain full rook placements on Ferrers boards, we give short proofs of two enumerative results.
Bloom, Jonathan, Vatter, Vince
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Discrete Mathematics & Theoretical Computer Science, 2017 The PASEP (Partially Asymmetric Simple Exclusion Process) is a probabilistic model of moving particles, which is of great interest in combinatorics, since it appeared that its partition function counts some tableaux.
Matthieu Josuat-Vergès
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Bijections on m-level Rook Placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Partition the rows of a board into sets of $m$ rows called levels. An $m$-level rook placement is a subset of squares of the board with no two in the same column or the same level.
Kenneth Barrese, Bruce Sagan
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q-Rook placements and Jordan forms of upper-triangular nilpotent matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The set of $n$ by $n$ upper-triangular nilpotent matrices with entries in a finite field $F_q$ has Jordan canonical forms indexed by partitions $λ \vdash n$. We study a connection between these matrices and non-attacking q-rook placements, which leads to
Martha Yip
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Matrix Ansatz, lattice paths and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP.
S. Corteel +3 more
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Journal of Combinatorial Theory - Series A, 2014 Goldman, Joichi, and White proved a beautiful theorem showing that the falling factorial generating function for the rook numbers of a Ferrers board factors over the integers. Briggs and Remmel studied an analogue of rook placements where rows are replaced by sets of $m$ rows called levels.
Jeffrey Remmel, Bruce E Sagan
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A generalization of Eulerian numbers via rook placements [PDF]
Involve, 2017 15 ...
Christopher Cox
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Rook placements and generalized partition varieties
Discrete Mathematics, 1997 The paper generalizes the concept of partition varieties introduced in a preceding paper by the same author. For this purpose, \(\gamma\)-compatible partitions \(\lambda\) are introduced, where \(\gamma\) is a composition of some integers. It is shown that a certain quotient space associated to such composition \(\gamma\) and partition \(\lambda\) is a
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Invisible permutations and rook placements on a Ferrers board
Discrete Mathematics, 1995 We study non-attacking rook placements on a Ferrers board by extending them to certain permutation matrices, called invisible permutations. By introducing a length function on rook placements, we define a rook length polynomial \(\text{RL}_ k(\lambda, q)\) for a given number \(k\) of rooks and a Ferrers board \(F_ \lambda\). We prove that \(\text{R}_ k(
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