Riordan Arrays - Barry, Paul

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Résumé :
The aim of this text is to introduce the beginner to the theory of Riordan arrays. Starting in a simple and constructive manner, the basic structure of these arrays is explained with clear examples, before a more theoretical grounding is provided. Ordinary Riordan arrays and exponential Riordan arrays are examined, with many explicit examples, and their applications to combinatorics and other areas are explored. The production matrix of a Riordan array is shown to play a key role, along with various sequence characterizations. Formal prerequisites are kept to a minimum, in order to provide a gentle introduction to this exciting area, that involves linear algebra, group theory and combinatorics. The reader will be well positioned to further explore Riordan arrays and their applications, and to undertake their own projects. They will join a community of interested mathematicians that now spans all continents, in a growing area of research and application....

Biographie:
Paul Barry, a blues harmonica player, promoter, and bandleader, was born and raised in St. Paul, Minnesota. Paul has fronted many bands over the years, playing and recording with Big Smokey Smothers, Willie Walker, and Mitch Kashmar among others. In 2016 Paul released a 1992 recording where he backed the legendary former Muddy Waters and Howlin' Wolf sideman Big Smokey Smothers. That's Alright received critical acclaim and was Smothers' final studio recording. Paul also released two albums under his own name: Talk Is Cheap in 2016 and Blow It Cool in 2018. The Paul Barry Blues Band, based in Minneapolis/St. Paul, specializes in Chicago and West Coast jump blues and plays locally in clubs and festivals in and around the state of Minnesota. Paul also is active in promoting blues in the Twin Cities area dating back to the late 1970s. He currently hosts an annual New Year's Eve blues celebration with nationally known blues artists. In his spare time, Paul is an avid tennis player and an awarding-winning high school tennis coach.

Sommaire:
The aim of this text is to introduce the beginner to the theory of Riordan arrays. Starting in a simple and constructive manner, the basic structure of these arrays is explained with clear examples, before a more theoretical grounding is provided. Ordinary Riordan arrays and exponential Riordan arrays are examined, with many explicit examples, and their applications to combinatorics and other areas are explored. The production matrix of a Riordan array is shown to play a key role, along with various sequence characterizations. Formal prerequisites are kept to a minimum, in order to provide a gentle introduction to this exciting area, that involves linear algebra, group theory and combinatorics. The reader will be well positioned to further explore Riordan arrays and their applications, and to undertake their own projects. They will join a community of interested mathematicians that now spans all continents, in a growing area of research and application....