The enumeration of planar graphs via Wick's theorem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A00206249" target="_blank" >RIV/00216208:11320/09:00206249 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

The enumeration of planar graphs via Wick's theorem

Popis výsledku v původním jazyce

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 thegraphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function.

Název v anglickém jazyce

The enumeration of planar graphs via Wick's theorem

Popis výsledku anglicky

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 thegraphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Mathematics

ISSN

0001-8708

e-ISSN

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Svazek periodika

221

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

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Kód UT WoS článku

000266374300009

EID výsledku v databázi Scopus

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