Results 1 to 10 of about 684 (87)
Rook Poset Equivalence of Ferrers Boards [PDF]
Order, 2006 A natural construction due to K. Ding yields Schubert varieties from Ferrers boards. The poset structure of the Schubert cells in these varieties is equal to the poset of maximal rook placements on the Ferrers board under the Bruhat order. We determine when two Ferrers boards have isomorphic rook posets. Equivalently, we give an exact categorization of
Mike Develin
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Simplicial complexes of triangular Ferrers boards [PDF]
Journal of Algebraic Combinatorics, 2012 We study the simplicial complex that arises from non-attacking rook placements on a subclass of Ferrers boards that have $a_i$ rows of length $i$ where $a_i>0$ and $i\leq n$ for some positive integer $n$. In particular, we will investigate enumerative properties of their facets, their homotopy type, and homology.
Clark, Eric, Zeckner, Matthew
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On criteria for rook equivalence of Ferrers boards [PDF]
European Journal of Combinatorics, 2019 In [2] we introduced a new notion of Wilf equivalence of integer partitions and proved that rook equivalence implies Wilf equivalence. In the present paper we prove the converse and thereby establish a new criterion for rook equivalence. We also refine two of the standard criteria for rook equivalence and establish another new one involving what we ...
Jonathan Bloom
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Rook Theory. I.: Rook Equivalence of Ferrers Boards [PDF]
Proceedings of the American Mathematical Society, 1975 We introduce a new tool, the factorial polynomials, to study rook equivalence of Ferrers boards. We provide a set of invariants for rook equivalence as well as a very simple algorithm for deciding rook equivalence of Ferrers boards. We then count the number of Ferrers boards rook equivalent to a given Ferrers board.
Dennis E White
exaly +2 more sources
Bruhat intervals as rooks on skew Ferrers boards
Journal of Combinatorial Theory - Series A, 2007 16 pages, 9 ...
exaly +3 more sources
The rook numbers of Ferrers boards and the related restricted permutation numbers
Journal of Statistical Planning and Inference, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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
doaj +1 more source
Derangements on a Ferrers board [PDF]
Discrete Mathematics, Algorithms and Applications, 2015 We study the derangement number on a Ferrers board B = (n × n) - λ with respect to an initial permutation M, that is, the number of permutations on B that share no common points with M. We prove that the derangement number is independent of M if and only if λ is of rectangular shape.
William Linz, Catherine Yan 0001
openaire +2 more sources
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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Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In their paper on Wilf-equivalence for singleton classes, Backelin, West, and Xin introduced a transformation $\phi^*$, defined by an iterative process and operating on (all) full rook placements on Ferrers boards. Bousquet-Mélou and Steingrimsson proved
Jonathan Bloom, Dan Saracino
doaj +1 more source