Header

UZH-Logo

Maintenance Infos

Jack polynomials and orientability generating series of maps


Dołęga, Maciej; Féray, Valentin; Śniady, Piotr (2014). Jack polynomials and orientability generating series of maps. Seminaire Lotharingien de Combinatoire (SLC), 70(50):online.

Abstract

We study Jack characters, which are the coefficients of the power-sum expansion of Jack symmetric functions with a suitable normalization. These quantities have been introduced by Lassalle who formulated some challenging conjectures about them. We conjecture the existence of a weight on non-oriented maps (i.e., graphs drawn on non-oriented surfaces) which allows to express any given Jack character as a weighted sum of some simple functions indexed by maps. We provide a candidate for this weight which gives a positive answer to our conjecture in some, but unfortunately not all, cases. In particular, it gives a positive answer for Jack characters specialized to Young diagrams of rectangular shape. This candidate weight attempts to measure, in a sense, the non-orientability of a given map.

Abstract

We study Jack characters, which are the coefficients of the power-sum expansion of Jack symmetric functions with a suitable normalization. These quantities have been introduced by Lassalle who formulated some challenging conjectures about them. We conjecture the existence of a weight on non-oriented maps (i.e., graphs drawn on non-oriented surfaces) which allows to express any given Jack character as a weighted sum of some simple functions indexed by maps. We provide a candidate for this weight which gives a positive answer to our conjecture in some, but unfortunately not all, cases. In particular, it gives a positive answer for Jack characters specialized to Young diagrams of rectangular shape. This candidate weight attempts to measure, in a sense, the non-orientability of a given map.

Statistics

Altmetrics

Downloads

0 downloads since deposited on 29 Jan 2015
0 downloads since 12 months

Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2014
Deposited On:29 Jan 2015 16:38
Last Modified:05 Apr 2016 18:47
Publisher:Institut de Recherche Mathematique Avancee, Strasbourg
ISSN:1286-4889
Free access at:Official URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1142/S0129167X1450038
Official URL:http://www.emis.de/journals/SLC/wpapers/s70sniady.pdf

Download

Preview Icon on Download
Content: Published Version
Filetype: PDF - Registered users only
Size: 473kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations