On (shape-)Wilf-equivalence for words

Guo, Taomei; Krattenthaler, Christian; Zhang, Yi

doi:10.1016/j.aam.2018.05.006

Cited by 3 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Of particular interest are the so-called transversal fillings, which contain exactly one 1-cell in each row and each column, and can be viewed as generalizations of permutation matrices. Transversal fillings of Ferrers shapes have played a crucial part in establishing most of the known results on Wilf equivalence [1,16], as well as in the study of many related combinatorial objects, such as involutions [2], words [7], matchings [9,12], graphs [5,6] or set partitions [4,11].…”

Section: Introductionmentioning

confidence: 99%

Fillings of skew shapes avoiding diagonal patterns

Jelínek,

Karpilovskij

2020

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Fillings of skew shapes avoiding diagonal patterns

Jelínek,

Karpilovskij

2020

Preprint

View full text Add to dashboard Cite

show abstract

Avoiding a pair of patterns in multisets and compositions

Jelínek¹,

Mansour²,

Ramírez³

et al. 2022

Advances in Applied Mathematics

View full text Add to dashboard Cite

Fillings of skew shapes avoiding diagonal patterns

Jelínek¹,

Karpilovskij²

2021

Discrete Mathematics &Amp; Theoretical Computer Science

View full text Add to dashboard Cite

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. Comment: 23 pages, 14 figures; formatting changes for publication in DMTCS, no changes in content

show abstract

On (shape-)Wilf-equivalence for words

Cited by 3 publications

References 11 publications

Fillings of skew shapes avoiding diagonal patterns

Fillings of skew shapes avoiding diagonal patterns

Avoiding a pair of patterns in multisets and compositions

Fillings of skew shapes avoiding diagonal patterns

Contact Info

Product

Resources

About