Change search
ReferencesLink to record
Permanent link

Direct link
Extended pattern avoidance
2002 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 246, no 03-jan, 219-230 p.Article in journal (Refereed) Published
Abstract [en]

A 0-1 matrix is said to be extendably tau-avoiding if it can be the upper left corner of a tau-avoiding permutation matrix. This concept arose in Eriksson and Linusson (Electron. J. Combin. 2 (1995) R6) where the surprising result that the number of extendably 321-avoiding rectangles are enumerated by the ballot numbers was proved, Here we study the other five patterns of length three. The main result is that the six patterns of length three divide into only two cases, no easy symmetry can explain this. Another result is that the Simion-Schmidt-West bijection for permutations avoiding patterns 12tau and 21tau works also for extended pattern avoidance. As an application, we use the results on extended pattern avoidance to prove a sequence of refinements on the enumeration of permutations avoiding patterns of length 3. The results and proofs use many properties and refinements of the Catalan numbers.

Place, publisher, year, edition, pages
2002. Vol. 246, no 03-jan, 219-230 p.
Keyword [en]
avoiding pattern, catalan number, ballot number
URN: urn:nbn:se:kth:diva-21373ISI: 000174330400013OAI: diva2:340071
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

Open Access in DiVA

No full text

Search in DiVA

By author/editor
Linusson, Svante
In the same journal
Discrete Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 12 hits
ReferencesLink to record
Permanent link

Direct link