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Chain-dependent Conditions in Extremal Set Theory
Order, 2023 AbstractIn extremal set theory our usual goal is to find the maximal size of a family of subsets of an n-element set satisfying a condition. A condition is called chain-dependent, if it is satisfied for a family if and only if it is satisfied for its intersections with the n! full chains.
Dániel T. Nagy, Kartal Nagy
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On some interconnections between combinatorial optimization and extremal graph theory [PDF]
Yugoslav Journal of Operations Research, 2004 The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set.
Cvetković Dragoš M. +2 more
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Capacities: From information theory to extremal set theory
Journal of Combinatorial Theory, Series A, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Korner, GARGANO, Luisa, VACCARO, Ugo
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An extremal problem on trees and database theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider an extremal problem on labelled directed trees and applications to database theory. Among others, we will show explicit keysystems on an underlying set of size $n$, that cannot be represented by a database of less than $2^{n(1-c\cdot \log ...
Gyula O.H. Katona, Krisztián Tichler
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Tangential extremal principles for finite and infinite systems of sets, I: basic theory [PDF]
Mathematical Programming, 2012 In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to ...
Boris S Mordukhovich +2 more
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Information Inequalities via Submodularity and a Problem in Extremal Graph Theory
Entropy, 2022 The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties.
Igal Sason
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Defect extremal surface as the holographic counterpart of Island formula
Journal of High Energy Physics, 2021 We propose defect extremal surface as the holographic counterpart of boundary quantum extremal surface. The defect extremal surface is defined by minimizing the Ryu-Takayanagi surface corrected by the defect theory.
Feiyu Deng, Jinwei Chu, Yang Zhou
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npj Quantum Information, 2022 The problem of achieving security of device-independent (or semi-device-independent) cryptography (for quantum key distribution and randomness generation) against the most general no-signaling adversaries has remained open.
Ravishankar Ramanathan +3 more
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Page curve from defect extremal surface and island in higher dimensions
Journal of High Energy Physics, 2021 Defect extremal surface (DES) is defined by minimizing the Ryu-Takayanagi surface corrected by the quantum theory localized on the defect, which is useful when the RT surface crosses or terminates on the defect. Based on the decomposition procedure of an
Jinwei Chu, Feiyu Deng, Yang Zhou
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“Mathematics is the Logic of the Infinite”: Zermelo’s Project of Infinitary Logic
Studies in Logic, Grammar and Rhetoric, 2021 In this paper I discuss Ernst Zermelo’s ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. The presentation of Zermelo’s ideas is accompanied with some remarks
Pogonowski Jerzy
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