Alexey Spiridonov - Pattern-Avoidance in Binary Fillings of Grid Shapes (short version)

dmtcs:3610 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3610
Pattern-Avoidance in Binary Fillings of Grid Shapes (short version)Article

Authors: Alexey Spiridonov 1

  • 1 Department of Mathematics [MIT]

A $\textit{grid shape}$ is a set of boxes chosen from a square grid; any Young diagram is an example. This paper considers a notion of pattern-avoidance for $0-1$ fillings of grid shapes, which generalizes permutation pattern-avoidance. A filling avoids some patterns if none of its sub-shapes equal any of the patterns. We focus on patterns that are $\textit{pairs}$ of $2 \times 2$ fillings. For some shapes, fillings that avoid specific $2 \times 2$ pairs are in bijection with totally nonnegative Grassmann cells, or with acyclic orientations of bipartite graphs. We prove a number of results analogous to Wilf-equivalence for these objects ―- that is, we show that for certain classes of shapes, some pattern-avoiding fillings are equinumerous with others.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: pattern-avoidance,filling,grid shape,Le-diagram,acyclic orientation,Young diagram,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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