Results 1 to 10 of about 11,244 (115)
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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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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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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Rook placements and Jordan forms of upper-triangular nilpotent matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 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 lambda of n.
Yip, Martha
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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
exaly +3 more sources
The spatial distribution of corvid nests in the urbanized environmental components (using the example of the Kirovsky district of Saratov) [PDF]
Известия Саратовского университета. Новая серия: Серия Химия. Биология. Экология, 2023 . This study is dedicated to the nest placement peculiarities of four species of the Corvidae family: the Jackdaw, Rook, Hooded Crow, and Eurasian Magpie – in the urbanized environmental components on the territory of the Kirovsky district of ...
Kuliseva, Yulia I. +1 more
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A Graph Theory of Rook Placements [PDF]
The Electronic Journal of Combinatorics, 2021 Two boards are rook equivalent if they have the same number of non-attacking rook placements for any number of rooks. Define a rook equivalence graph on an equivalence class of Ferrers boards by specifying that two boards are connected by an edge if you can obtain one of the boards by moving squares in the other board out of one column and into a ...
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Combinatorics of diagrams of permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 There are numerous combinatorial objects associated to a Grassmannian permutation $w_λ$ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook placements, acyclic orientations, various restricted fillings) and ...
Joel Brewster Lewis, Alejandro Morales
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Negative $q$-Stirling numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The notion of the negative $q$-binomial was recently introduced by Fu, Reiner, Stanton and Thiem. Mirroring the negative $q$-binomial, we show the classical $q$ -Stirling numbers of the second kind can be expressed as a pair of statistics on a subset of ...
Yue Cai, Margaret Readdy
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Gradedness of the set of rook placements in A n−1 [PDF]
Communications in Mathematics, 2021 Abstract A rook placement is a subset of a root system consisting of positive roots with pairwise non-positive inner products. To each rook placement in a root system one can assign the coadjoint orbit of the Borel subgroup of a reductive algebraic group with this root system.
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