Results 1 to 10 of about 56,648 (187)
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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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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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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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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On the Spectra of Simplicial Rook Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The $\textit{simplicial rook graph}$ $SR(d,n)$ is the graph whose vertices are the lattice points in the $n$th dilate of the standard simplex in $\mathbb{R}^d$, with two vertices adjacent if they differ in exactly two coordinates.
Jeremy L. Martin, Jennifer D. Wagner
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A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We describe a combinatorial model for the $q$-analogs of the generalized Stirling numbers in terms of bugs and colonies. Using both algebraic and combinatorial methods, we derive explicit formulas, recursions and generating functions for these $q ...
Miguel Méndez, Adolfo Rodríguez
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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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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
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Type B (p, q)-Stirling Numbers via Signed Restricted Growth Functions and Rook Theory
MathematicsStirling numbers are among the most classical objects in enumerative combinatorics, counting set partitions and permutations. In this paper, we study their (p,q)-analogues in type B from a rook-theoretic point of view. We introduce a type B Ferrers board
Hasan Arslan +3 more
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