Fillings of skew shapes avoiding diagonal patterns
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436732" target="_blank" >RIV/00216208:11320/21:10436732 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CrDnatsRFT" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CrDnatsRFT</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.46298/DMTCS.6171" target="_blank" >10.46298/DMTCS.6171</a>
Alternative languages
Result language
angličtina
Original language name
Fillings of skew shapes avoiding diagonal patterns
Original language description
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 southeast 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-19158S" target="_blank" >GA18-19158S: Algorithmic, structural and complexity aspects of geometric and other configurations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete Mathematics and Theoretical Computer Science
ISSN
1462-7264
e-ISSN
1365-8050
Volume of the periodical
22
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
23
Pages from-to
8
UT code for WoS article
001073436700004
EID of the result in the Scopus database
2-s2.0-85116002996