Reference number : GC-2017-Q1-01589, amendment number : , agreement type : G, recipient legal name : Currie, James (The University of Winnipeg), recipient country : CA, recipient province : nan, recipient city : Manitoba, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : In the modern world, long sequences of symbols over small alphabets are of basic importance. Whether we are considering streams of 0's and 1's over the internet, or considering long DNA sequences made up from the letters A, C, G, T, understanding the mathematics of strings of symbols is of basic importance. This research studies the regularities and irregularities in long strings of symbols, identifying which patterns must always arise, and which can be avoided. The simplest patterns, repetitions, play a key role in data compression, such as we see every day in .zip files. More complicated patterns, involving repetitions and reversals, arise naturally in the study of genetic sequences in DNA or RNA, in so-called "DNA hairpins". Words avoiding patterns have also been proposed as a cryptographic tool. 
 
Simple questions about which patterns can be avoided in long strings of symbols remain unanswered, but problems which had been previously unsolved for 20 or 40 years are starting to be resolved. In the same way that studying simple objects in arithmetic, such as prime numbers, has led to technical breakthroughs in encryption of banking transactions, understanding the basic mathematics of strings of symbols should continue to have importance in data compression, genetic analysis and information technology., program purpose french : In the modern world, long sequences of symbols over small alphabets are of basic importance. Whether we are considering streams of 0's and 1's over the internet, or considering long DNA sequences made up from the letters A, C, G, T, understanding the mathematics of strings of symbols is of basic importance. This research studies the regularities and irregularities in long strings of symbols, identifying which patterns must always arise, and which can be avoided. The simplest patterns, repetitions, play a key role in data compression, such as we see every day in .zip files. More complicated patterns, involving repetitions and reversals, arise naturally in the study of genetic sequences in DNA or RNA, in so-called "DNA hairpins". Words avoiding patterns have also been proposed as a cryptographic tool. 
 
Simple questions about which patterns can be avoided in long strings of symbols remain unanswered, but problems which had been previously unsolved for 20 or 40 years are starting to be resolved. In the same way that studying simple objects in arithmetic, such as prime numbers, has led to technical breakthroughs in encryption of banking transactions, understanding the basic mathematics of strings of symbols should continue to have importance in data compression, genetic analysis and information technology., agreement title english : Extendibility and growth of words avoiding patterns, agreement title french : Extendibility and growth of words avoiding patterns, agreement number : RGPIN, agreement value : 70000.0, agreement start date : 2017-05-10, agreement end date : nan, description english : nan, description french : nan, expected results english : nan, expected results french : nan, additional information english : Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023), additional information french : Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023), owner organization : nserc-crsng, owner organization title : Natural Sciences and Engineering Research Council of Canada | Conseil de recherches en sciences naturelles et en génie du Canada