Titlebook: Eulerian Numbers; T. Kyle Petersen Textbook 2015 Springer Science+Business Media New York 2015 Catalan numbers.Coxeter groups.Eulerian num

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https://doi.org/10.1007/978-3-7091-9922-0In this supplemental chapter we will find the Eulerian numbers cropping up in some surprising places.

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Institutsgeschichte als Familiengeschichte?. have arisen is in combinatorial topology. In this chapter we will put some of our previous work in the context of the study of simplicial complexes. While there is some assumed familiarity with topological concepts, no formal topological background is required for understanding this chapter.

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https://doi.org/10.1007/978-3-658-06970-4. in geometry and topology. It is an operation that preserves topology and is well-behaved combinatorially. In this chapter we will study a transformation of Brenti and Welker that maps the .-vector of a complex to the .-vector of its barycentric subdivision.

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Eulerian numbers. of numbers a typical mathematics student encounters is Pascal’s triangle, shown in Table 1.1. It has many beautiful properties, some of which we will review shortly. One of the main points of this chapter is to argue that the array of Eulerian numbers is just as interesting as Pascal’s triangle.

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Refined enumeration. Often, the way we count allows us to keep track of more than one permutation statistic without any extra effort. In particular we consider various ways to pair a statistic with an Eulerian distribution with another statistic having a Mahonian distribution. Similar ideas are explored for Catalan objects.

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