منابع مشابه
Combinatorial Gems
Although this lecture does not contain many offical Olympiad problems, the arguments which are used are all common elements of Olympiad problem solving. Some of these perhaps could have made nice Olympiad problems, if not for the fact that they were already well-known due to their importance in higher mathematics. Most of this is sourced from the excellent combinatorics course developed by Benn...
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fatalities in the 1970s and 80s were due to fishing equipment. It is not that these threats went unrecognised. Aside from a brief spell during Mao’s Great Leap Forward — when Nature was declared an ‘enemy of the people’ and the Baiji was actively prosecuted — the urgent need for its conservation was gradually realised inside and outside of China. But, while some attempts were made to establish ...
متن کاملCs-621 Theory Gems
So far, we were focusing on “static” analysis of games. That is, we considered scenarios in which the game and utilities of all the players are fixed and known and our task is only to predict possible outcomes of that game when some (or all) the players are acting rationally. Today, we turn the tables: there is no predefined game, only players that have some utilities. However, the key point is...
متن کاملFour Quotient Set Gems
Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the MONTHLY, despite its intense coverage of quotient sets over the years. Introduction If A is a subset of the natural numbers N = {1, 2, . . .}, then we let R(A) = {a/a : a, a ∈ A} denote the corresponding quotient set (sometimes called a ratio set). Our aim in this...
متن کاملCs-621 Theory Gems
As we mentioned in the last lecture, one of the core components of our algorithm for distinct elements problem is a space-efficient construction of 2-wise independent functions. Formally, a k-wise independent hash function f : [m]→ [T ] is a randomized function that provides the guarantee that, for any k distinct elements j1, . . . , jk ∈ [m] and any k possible values t1, . . . , tk ∈ [T ], the...
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ژورنال
عنوان ژورنال: Cell Cycle
سال: 2014
ISSN: 1538-4101,1551-4005
DOI: 10.4161/cc.27788