000			04008nam a22003978i 4500
001			CR9780511803895
003			UkCbUP
005			20200124160225.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			101021s2009||||enk o ||1 0|eng|d
020			_a9780511803895 (ebook)
020			_z9780521883894 (hardback)
020			_z9780521737944 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA164 _b.K86 2009
082	0	0	_a511/.6 _222
100	1		_aKung, Joseph P. S., _eauthor.
245	1	0	_aCombinatorics : _bthe Rota way / _cJoseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan.
264		1	_aCambridge : _bCambridge University Press, _c2009.
300			_a1 online resource (xii, 396 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge mathematical library
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tSets, Functions, and Relations. Sets, valuations, and Boolean algebras -- _tPartially ordered sets -- _tLattices -- _tFunctions, partitions, and entropy -- _tRelations -- _tMatching Theory. What is matching theory? -- _tThe marriage theorem -- _tFree and incidence matrices -- _tSubmodular functions and independent matchings -- _tRado's theorem on subrelations -- _tDoubly stochastic matrices -- _tThe Gale-Ryser theorem -- _tMatching theory in higher dimensions -- _tPartially Ordered Sets and Lattices. Möbius functions -- _tChains and antichains -- _tSperner theory -- _tModular and linear lattices -- _tFinite modular and geometric lattices -- _tValuation rings and Möbius algebras -- _tGenerating Functions and the Umbral Calculus. Generating functions -- dt Elementary umbral calculus -- _tPolynomial sequences of binomial type -- _tSheffer sequences -- _tUmbral composition and connection matrices -- _tThe Riemann zeta function -- _tSymmetric Functions and Baxter Algebras. Symmetric functions -- _tDistribution, occupancy, and the partition lattice -- _tEnumeration under a group action -- _tBaxter operators -- _tFree Baxter algebras -- _tIdentities in Baxter algebras -- _tSymmetric functions over finite fields -- _tHistorical remarks and further reading -- _tDeterminants, Matrices, and Polynomials. Polynomials -- _tApolarity -- _tGrace's theorem -- _tMultiplier sequences -- _tTotally positive matrices -- _tExterior algebras and compound matrices -- _tEigenvalues of totally positive matrices -- _tVariation decreasing matrices -- _tPólya frequency sequences -- _tSelected Solutions.
520			_aGian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.
650		0	_aCombinatorial analysis.
600	1	0	_aRota, Gian-Carlo, _d1932-1999.
700	1		_aRota, Gian-Carlo, _d1932-1999, _eauthor.
700	1		_aYan, Catherine H., _eauthor.
776	0	8	_iPrint version: _z9780521883894
830		0	_aCambridge mathematical library.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511803895
999			_c517103 _d517101