A labelled variant of the matchings-Jack and hypermap-jack conjectures

Andrei L. Kanunnikov; Valentin V. Promyslov; Ekaterina A. Vassilieva

A labelled variant of the matchings-Jack and hypermap-jack conjectures

Andrei L. Kanunnikov
, Valentin V. Promyslov
, Ekaterina A. Vassilieva

Moscow State University

Research output: Contribution to conference › Paper › peer-review

Abstract

Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack and hypermap-Jack conjectures are two major open questions relating symmetric functions, representation theory and combinatorial maps. These conjectures state an important combinatorial interpretation of the coefficients in the power sum expansion of two related formal power series involving Jack symmetric functions. These coefficients are indexed by three partitions of a given integer n. This paper is devoted to the case when one of them is equal to (n). We exhibit some of their polynomial properties and prove a variant of the two conjectures involving labelled hypermaps and matchings in some important cases.

Original language	English
Publication status	Published - 1 Jan 2018
Event	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States Duration: 16 Jul 2018 → 20 Jul 2018

Conference

Conference	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
Country/Territory	United States
City	Hanover
Period	16/07/18 → 20/07/18

Keywords

Jack symmetric functions
Matchings-Jack and hypermap-Jack conjectures

Cite this

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title = "A labelled variant of the matchings-Jack and hypermap-jack conjectures",

abstract = "Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack and hypermap-Jack conjectures are two major open questions relating symmetric functions, representation theory and combinatorial maps. These conjectures state an important combinatorial interpretation of the coefficients in the power sum expansion of two related formal power series involving Jack symmetric functions. These coefficients are indexed by three partitions of a given integer n. This paper is devoted to the case when one of them is equal to (n). We exhibit some of their polynomial properties and prove a variant of the two conjectures involving labelled hypermaps and matchings in some important cases.",

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author = "Kanunnikov, \{Andrei L.\} and Promyslov, \{Valentin V.\} and Vassilieva, \{Ekaterina A.\}",

note = "Publisher Copyright: {\textcopyright} FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.; 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 ; Conference date: 16-07-2018 Through 20-07-2018",

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TY - CONF

T1 - A labelled variant of the matchings-Jack and hypermap-jack conjectures

AU - Kanunnikov, Andrei L.

AU - Promyslov, Valentin V.

AU - Vassilieva, Ekaterina A.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack and hypermap-Jack conjectures are two major open questions relating symmetric functions, representation theory and combinatorial maps. These conjectures state an important combinatorial interpretation of the coefficients in the power sum expansion of two related formal power series involving Jack symmetric functions. These coefficients are indexed by three partitions of a given integer n. This paper is devoted to the case when one of them is equal to (n). We exhibit some of their polynomial properties and prove a variant of the two conjectures involving labelled hypermaps and matchings in some important cases.

AB - Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack and hypermap-Jack conjectures are two major open questions relating symmetric functions, representation theory and combinatorial maps. These conjectures state an important combinatorial interpretation of the coefficients in the power sum expansion of two related formal power series involving Jack symmetric functions. These coefficients are indexed by three partitions of a given integer n. This paper is devoted to the case when one of them is equal to (n). We exhibit some of their polynomial properties and prove a variant of the two conjectures involving labelled hypermaps and matchings in some important cases.

KW - Jack symmetric functions

KW - Matchings-Jack and hypermap-Jack conjectures

M3 - Paper

AN - SCOPUS:85089345611

T2 - 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018

Y2 - 16 July 2018 through 20 July 2018

ER -

A labelled variant of the matchings-Jack and hypermap-jack conjectures

Abstract

Conference

Keywords

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Cite this