000			03238cam a2200469 i 4500
001			on1413943532
003			OCoLC
005			20240516153410.0
008			231214t20232023riua b 000 0 eng d
020			_a1470462680 _q(paperback)
020			_a9781470462680 _q(paperback)
035			_a(OCoLC)1413943532
040			_aYDX _beng _erda _cYDX _dYSM _dOCLCO _dUNBCA _dCLU _dBUB _dOCLCO _dEAU _dOCLCQ
066			_c(S
082	0	4	_a511.33 _qOCoLC
090			_acolm
100	1		_aPétréolle, Mathias, _eauthor
245	1	0	_aLattice paths and branched fractions : _ban infinite sequence of generalizations of the Stieltjes-Rogers and Thron-Rogers polynomials, with coefficientwise Hankel-total positivity / _cMathias Pétréolle, Alan D. Sokal, Bao-Xuan Zhu.
264		1	_aProvidence, Rhode Island : _bAmerican Mathematical Society, _c[2023]
264		4	_c©2023
300			_av, 154 pages : _billustrations ; _c26 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vnumber 1450
500			_a"November 2023, volume 291, number 1450 (fifth of 5 numbers)."
504			_aIncludes bibliographical references (pages 147-154).
650		0	_aLattice paths.
650		0	_aPolynomials.
650		0	_aFractions.
650		6	_aChemins de treillis.
650		6	_aPolynômes.
650		6	_aFractions.
697			_923736 _aColeções de Monografias.
700	1		_aSokal, Alan D., _d1955- _eauthor. _1https://id.oclc.org/worldcat/entity/E39PBJfGVgk6WWWRy8bkrGy68C
700	1		_aZhu, Bao-Xuan, _eauthor
830		0	_aMemoirs of the American Mathematical Society ; _vv. 1450.
880	3		_6520-00/(S _a"We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1, of the Stieltjes-Rogers and Thron-Rogers polynomials; they arise as the power-series expansions of some branched continued fractions, and as the generating polynomials for m-Dyck and m-Schr¨oder paths with height-dependent weights. We prove that all of these sequences of polynomials are coefficientwise Hankel totally positive, jointly in all the (infinitely many) indeterminates. We then apply this theory to prove the coefficientwise Hankel-total positivity for combinatorially interesting sequences of polynomials. Enumeration of unlabeled ordered trees and forests gives rise to multivariate Fuss-Narayana polynomials and Fuss-Narayana symmetric functions. Enumeration of increasing (labeled) ordered trees and forests gives rise to multivariate Eulerian polynomials and Eulerian symmetric functions, which include the univariate mth-order Eulerian polynomials as specializations. We also find branched continued fractions for ratios of contiguous hypergeometric series rFs for arbitrary r and s, which generalize Gauss' continued fraction for ratios of contiguous 2F1; and for s = 0 we prove the coefficientwise Hankel-total positivity. Finally, we extend the branched continued fractions to ratios of contiguous basichypergeometric series rφs." -- Provided by publisher
942			_2ddc _cBK _n0
948			_hNO HOLDINGS IN P5A - 12 OTHER HOLDINGS
999			_c41145 _d41145