By T. Kyle Petersen
This textual content offers the Eulerian numbers within the context of contemporary enumerative, algebraic, and geometric combinatorics. The booklet first experiences Eulerian numbers from a merely combinatorial standpoint, then embarks on a travel of ways those numbers come up within the examine of hyperplane preparations, polytopes, and simplicial complexes. a few themes contain 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 booklet additionally contains 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 speak about how either the Eulerian and Narayana numbers have analogues in any finite Coxeter crew, with some of the comparable enumerative and geometric properties. There are 4 supplemental chapters all through, which survey extra complicated issues, 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 profit about these topics for the 1st time.
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Eulerian Numbers (Birkhäuser Advanced Texts Basler Lehrbücher) by T. Kyle Petersen