By Richard P. Stanley,Fomin Sergey
By Richard P. Stanley,Fomin Sergey
By Branislav Kisacanin
By Türker Biyikoglu,Josef Leydold,Peter F. Stadler
This interesting quantity investigates the constitution of eigenvectors and appears on the variety of their signal graphs ("nodal domains"), Perron parts, and graphs with extremal homes with recognize to eigenvectors. The Rayleigh quotient and rearrangement of graphs shape the most technique. Eigenvectors of graph Laplacians could seem a stunning subject for a e-book, however the authors express that there are refined ameliorations among the houses of strategies of Schrödinger equations on manifolds at the one hand, and their discrete analogs on graphs.
By T. Kyle Petersen
This textual content offers the Eulerian numbers within the context of recent enumerative, algebraic, and geometric combinatorics. The publication first stories Eulerian numbers from a only combinatorial perspective, then embarks on a travel of ways those numbers come up within the research of hyperplane preparations, polytopes, and simplicial complexes. a few issues comprise a radical 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 comparable enumerative and geometric properties. There are 4 supplemental chapters all through, which survey extra complex themes, 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.
By Patrick Knupp,Kambiz Salari
By Saber N. Elaydi
Incorporating quite a few new issues and know-how no longer present in related texts, Discrete Chaos, moment Edition offers an intensive, up to date remedy of the idea and functions of discrete dynamical systems.
By Jeffrey Remmel,Anthony Mendes
This monograph presents a self-contained creation to symmetric services and their use in enumerative combinatorics. it's the first booklet to discover the various tools and effects that the authors current. a number of workouts are integrated all through, in addition to complete strategies, to demonstrate strategies and in addition spotlight many fascinating mathematical ideas.
The textual content starts off via introducing basic combinatorial gadgets corresponding to diversifications and integer walls, in addition to producing functions. Symmetric services are thought of within the subsequent bankruptcy, with a special emphasis at the combinatorics of the transition matrices among bases of symmetric functions. bankruptcy three makes use of this introductory fabric to explain how to define an collection of producing features for permutation statistics, after which those ideas are prolonged to discover producing services for quite a few gadgets in bankruptcy 4. the subsequent chapters current the Robinson-Schensted-Knuth set of rules and a mode for proving Pólya’s enumeration theorem utilizing symmetric functions. Chapters 7 and eight are extra really expert than the previous ones, masking consecutive trend suits in diversifications, phrases, cycles, and alternating variations and introducing the reciprocity strategy with a purpose to outline ring homomorphisms with fascinating properties.
Counting with Symmetric Functions will attract graduate scholars and researchers in arithmetic or comparable matters who're drawn to counting tools, producing services, or symmetric functions. the original method taken and effects and workouts explored by way of the authors make it a big contribution to the mathematical literature.
By Tadahito Harima,Toshiaki Maeno,Hideaki Morita,Yasuhide Numata,Akihito Wachi,Junzo Watanabe
By L. Lovász,J. Pelikán,K. Vesztergombi
Aimed at undergraduate arithmetic and desktop technological know-how scholars, this e-book is a superb advent to lots of difficulties of discrete arithmetic. It discusses a few chosen effects and strategies, quite often from parts of combinatorics and graph idea, and it makes use of proofs and challenge fixing to aid scholars comprehend the ideas to difficulties. various examples, figures, and routines are unfold through the book.
By M. M. Deza,P. Frankl,I. G. Rosenberg