uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Weighted Random Staircase Tableaux
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 23, no 6, 1114-1147 p.Article in journal (Refereed) Published
Abstract [en]

This paper concerns a relatively new combinatorial structure called staircase tableaux. They were introduced in the context of the asymmetric exclusion process and Askey-Wilson polynomials; however, their purely combinatorial properties have gained considerable interest in the past few years. In this paper we further study combinatorial properties of staircase tableaux. We consider a general model of random staircase tableaux in which symbols (Greek letters) that appear in staircase tableaux may have arbitrary positive weights. (We consider only the case with the parameters u = q = 1.) Under this general model we derive a number of results. Some of our results concern the limiting laws for the number of appearances of symbols in a random staircase tableaux. They generalize and subsume earlier results that were obtained for specific values of the weights. One advantage of our generality is that we may let the weights approach extreme values of zero or infinity, which covers further special cases appearing earlier in the literature. Furthermore, our generality allows us to analyse the structure of random staircase tableaux, and we obtain several results in this direction. One of the tools we use is the generating functions of the parameters of interest. This leads us to a two-parameter family of polynomials, generalizing the classical Eulerian polynomials. We also briefly discuss the relation of staircase tableaux to the asymmetric exclusion process, to other recently introduced types of tableaux, and to an urn model studied by a number of researchers, including Philippe Flajolet.

Place, publisher, year, edition, pages
2014. Vol. 23, no 6, 1114-1147 p.
National Category
URN: urn:nbn:se:uu:diva-237284DOI: 10.1017/S0963548314000327ISI: 000343755200008OAI: oai:DiVA.org:uu-237284DiVA: diva2:768378
Available from: 2014-12-03 Created: 2014-12-01 Last updated: 2014-12-03Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Janson, Svante
By organisation
Department of Mathematics
In the same journal
Combinatorics, probability & computing

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

Altmetric score

Total: 185 hits
ReferencesLink to record
Permanent link

Direct link