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X-WR-CALDESC:Events for Ashoka University
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DTSTART;TZID=UTC:20210914T163000
DTEND;TZID=UTC:20210914T173000
DTSTAMP:20211013T050519Z
CREATED:20210928T021222Z
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UID:19464-1631637000-1631640600@www.ashoka.edu.in
SUMMARY:Generating Functions Associated to Species of Structures
DESCRIPTION:Abstract: Species of structures were introduced by André Joyal and his group in Québec in the 1980s. They provide a way of organizing classes of labeled combinatorial objects that elevate the art of studying their generating functions to a science. \nCombinatorial relationships realized bijectively among such classes are transformed into functional relationships of their generating functions. For example\, from the combinatorial interpretation of a set partition as a set of non-empty sets\, the exponential generating function for Bell numbers exp(exp(z)-1) becomes blindingly clear; exp(z) is the generating function of sets and exp(z)-1 that of non-empty ones.\nI will discuss species of structures and some generating functions that are associated with them. I will explain how algebraic operations on generating functions can be seen to arise from set-theoretic operations on species. I will introduce the Frobenius characteristic generating function of a species of structures\, which is a simple variation of the cycle index generating function\, landing us in the world of symmetric polynomials.\nLecture Slides
URL:https://www.ashoka.edu.in/event/generating-functions-associated-to-species-of-structures/
CATEGORIES:Online Event
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