The Asymptotic Combinatorics of Permutations and Flag Algebras

• Grant number: 13/23720-9
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2014
• End date: August 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Yoshiharu Kohayakawa
• Grantee: Leonardo Nagami Coregliano
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science, AP.TEM
• Associated scholarship(s): 14/15134-5 - Permutations and flag algebras, BE.EP.MS

Abstract

This is the project for the master's degree of Leonardo Nagami Coregliano, to be developed under the supervision of Y. Kohayakawa, at the Instituto de Matemática e Estatística, USP, from February 2014 to July 2015 (18 months).This project has as main focus the asymptotic study of combinatorial structures, with emphasis on permutations, through the theory of Flag Algebras, developed by Razborov.The project has as starting point works on subpermutations of Albert, Atkinson, Handley, Holton, Král', Myers, Pikhurko and Stromquist, among others, and works developed using Flag Algebras on dense graphs and uniform hypergraphs of Das, Frankl, Huang, Kato, Katona, Ma, Naves, Razborov, Sudakov and Tokushige.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

COREGLIANO, LEONARDO NAGAMI. Quasi-carousel tournaments. JOURNAL OF GRAPH THEORY, v. 88, n. 1, p. 192-210, MAY 2018. (13/23720-9, 14/15134-5)

BASTOS, JOSEFRAN DE OLIVEIRA; COREGLIANO, LEONARDO NAGAMI. Packing densities of layered permutations and the minimum number of monotone sequences in layered permutations. DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, v. 18, n. 2, 2016. (13/23720-9)

COREGLIANO, LEONARDO NAGAMI; RAZBOROV, ALEXANDER A.. On the Density of Transitive Tournaments. JOURNAL OF GRAPH THEORY, v. 85, n. 1, p. 12-21, MAY 2017. (13/23720-9, 14/15134-5)

COREGLIANO, LEONARDO N.; PARENTE, ROBERTO F.; SATO, CRISTIANE M.. On the maximum density of fixed strongly connected subtournaments. ELECTRONIC JOURNAL OF COMBINATORICS, v. 26, n. 1, MAR 22 2019. (13/23720-9)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

COREGLIANO, Leonardo Nagami. Flag algebras and tournaments. 2015. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.