About: The enumeration of planar graphs via Wick's theorem

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Description	A seminal technique of theoretical physics called Wick's theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by their Euler characteristics. This leads to the map enumeration results analogous to those obtained by combinatorial methods. In this paper we show that the enumeration of the graphs embeddable on a given 2-dimensional surface (a main research topic of contemporary enumerative combinatories) can also be formulated as the Gaussian matrix integral of an ice-type partition function. Some of the most puzzling conjectures of discrete mathematics are related to the notion of the cycle double cover. We express the number of the graphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function. A seminal technique of theoretical physics called Wick's theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by their Euler characteristics. This leads to the map enumeration results analogous to those obtained by combinatorial methods. In this paper we show that the enumeration of the graphs embeddable on a given 2-dimensional surface (a main research topic of contemporary enumerative combinatories) can also be formulated as the Gaussian matrix integral of an ice-type partition function. Some of the most puzzling conjectures of discrete mathematics are related to the notion of the cycle double cover. We express the number of the graphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function. (en)
Title	The enumeration of planar graphs via Wick's theorem The enumeration of planar graphs via Wick's theorem (en)
skos:prefLabel	The enumeration of planar graphs via Wick's theorem The enumeration of planar graphs via Wick's theorem (en)
skos:notation	RIV/00216208:11320/09:00206249!RIV10-MSM-11320___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0545), Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Loebl, Martin
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	313344
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/09:00206249
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	enumeration; planar; graphs; Wick's; theorem (en)
http://linked.open.../riv/klicoveSlovo	graphs theorem planar enumeration Wick's
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[DEEC4E9756F0]
http://linked.open...i/riv/nazevZdroje	Advances in Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	221
http://linked.open...iv/tvurceVysledku	Loebl, Martin Kang, Mihyun
http://linked.open...ain/vavai/riv/wos	000266374300009
http://linked.open...n/vavai/riv/zamer	Moderní metody, struktury a systémy informatiky
issn	0001-8708
number of pages	22 (xsd:int)
http://localhost/t...ganizacniJednotka	11320
is http://linked.open...avai/riv/vysledek of	The enumeration of planar graphs via Wick's theorem The enumeration of planar graphs via Wick's theorem The enumeration of planar graphs via Wick's theorem The enumeration of planar graphs via Wick's theorem

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