This textual content offers the Eulerian numbers within the context of recent enumerative, algebraic, and geometric combinatorics. The ebook first experiences Eulerian numbers from a only combinatorial viewpoint, then embarks on a journey of ways those numbers come up within the examine of hyperplane preparations, polytopes, and simplicial complexes. a few issues comprise an intensive dialogue of gamma-nonnegativity and real-rootedness for Eulerian polynomials, in addition to the vulnerable order and the shard intersection order of the symmetric group.
The publication additionally encompasses a parallel tale of Catalan combinatorics, in which the Eulerian numbers are changed with Narayana numbers. back there's a development from combinatorics to geometry, together with dialogue of the associahedron and the lattice of noncrossing partitions.
The ultimate chapters talk about how either the Eulerian and Narayana numbers have analogues in any finite Coxeter workforce, with a number of the related enumerative and geometric properties. There are 4 supplemental chapters all through, which survey extra complex subject matters, together with a few open difficulties in combinatorial topology.
This textbook will serve a source for specialists within the box in addition to for graduate scholars and others hoping to benefit about these topics for the 1st time.
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