Vít Jelínek ; Mark Karpilovskij - Fillings of skew shapes avoiding diagonal patterns

dmtcs:6171 - Discrete Mathematics & Theoretical Computer Science, June 18, 2021, vol. 22 no. 2, Permutation Patterns 2019
Fillings of skew shapes avoiding diagonal patterns

Authors: Vít Jelínek ; Mark Karpilovskij

A skew shape is the difference of two top-left justified Ferrers shapes sharing the same top-left corner. We study integer fillings of skew shapes. As our first main result, we show that for a specific hereditary class of skew shapes, which we call D-free shapes, the fillings that avoid a north-east chain of size $k$ are in bijection with fillings that avoid a south-east chain of the same size. Since Ferrers shapes are a subclass of D-free shapes, this result can be seen as a generalization of previous analogous results for Ferrers shapes. As our second main result, we construct a bijection between 01-fillings of an arbitrary skew shape that avoid a south-east chain of size 2, and the 01-fillings of the same shape that simultaneously avoid a north-east chain of size 2 and a particular non-square subfilling. This generalizes a previous result for transversal fillings.


Volume: vol. 22 no. 2, Permutation Patterns 2019
Section: Special issues
Published on: June 18, 2021
Submitted on: February 28, 2020
Keywords: Mathematics - Combinatorics,Computer Science - Discrete Mathematics,05A05 (Primary), 05B50 (Secondary)


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