Counting contours on trees

Noga Alon; Rodrigo Bissacot; Eric Ossami Endo

doi:10.1007/s11005-016-0927-6

Counting contours on trees

Noga Alon, Rodrigo Bissacot^*, Eric Ossami Endo

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We calculate the exact number of contours of size n containing a fixed vertex in d-ary trees and provide sharp estimates for this number for more general trees. We also obtain a characterization of the locally finite trees with infinitely many contours of the same size containing a fixed vertex.

Original language	English
Pages (from-to)	887-899
Number of pages	13
Journal	Letters in Mathematical Physics
Volume	107
Issue number	5
DOIs	https://doi.org/10.1007/s11005-016-0927-6
State	Published - 1 May 2017

Funding

Funders	Funder number
Dutch stochastics cluster STAR
United States-Israel Binational Science Foundation	2012/107
Fundação de Amparo à Pesquisa do Estado de São Paulo	2016/08518-7, 11/16265-8
Conselho Nacional de Desenvolvimento Científico e Tecnológico	15/14434-8, 486819/2013-2, 312112/2015-7, 14/10637-9
Israel Science Foundation	620/13

Keywords

Catalan numbers
Contours
Cut Sets
Peierls
Trees

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10.1007/s11005-016-0927-6

Cite this

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title = "Counting contours on trees",

abstract = "We calculate the exact number of contours of size n containing a fixed vertex in d-ary trees and provide sharp estimates for this number for more general trees. We also obtain a characterization of the locally finite trees with infinitely many contours of the same size containing a fixed vertex.",

keywords = "Catalan numbers, Contours, Cut Sets, Peierls, Trees",

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AU - Alon, Noga

AU - Bissacot, Rodrigo

AU - Endo, Eric Ossami

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AB - We calculate the exact number of contours of size n containing a fixed vertex in d-ary trees and provide sharp estimates for this number for more general trees. We also obtain a characterization of the locally finite trees with infinitely many contours of the same size containing a fixed vertex.

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KW - Contours

KW - Cut Sets

KW - Peierls

KW - Trees

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Counting contours on trees

Abstract

Funding

Keywords

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