Báo cáo toán học: "Consecutive Patterns: From Permutations to Column-Convex Polyominoes and Back" ppsx

Báo cáo toán học: "Consecutive Patterns: From Permutations to Column-Convex Polyominoes and Back" ppsx

Báo cáo toán học: "Consecutive Patterns: From Permutations to Column-Convex Polyominoes and Back" ppsx

... y-ordinate from the bottom edge of Q k+1 to the top edge of Q k . For Q in Diagr am 3, δ(Q) =  2 3 6 4 4 5 3 2 3 5 5 2 6 5 4 1  . The map δ is a bijection from CCP to Y. As such, δ allows CCPs to be ... to a bipartition of N 2 . In this section, we use their Pattern Algebra to obtain a q-analog of Kitaev’s [25] Theorem 30 and to deduce a better generating function for per...
Ngày tải lên : 08/08/2014, 12:22
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Báo cáo toán học: "Repeated Patterns of Dense Packings of Equal Disks in a Square." pptx

Báo cáo toán học: "Repeated Patterns of Dense Packings of Equal Disks in a Square." pptx

... combinatorics 3 (1996), #R16 17 [GL1] R. L. Graham and B. D. Lubachevsky, Dense packings of equal disks in an equilateral triangle: from2 2to3 4andbeyond,The Electronic Journ. of Combinatorics ... =2,3,4,5,6 ,and7 (n = 5, 10, 18, 27, 39, and 52) and those packings (shown in Figs 2.9, 2.2, 2.5, and 2.8) are, indeed, optimal, except the case of n =10: proved[GMPW]forn = 5, 10, 18 and...
Ngày tải lên : 07/08/2014, 06:20
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Báo cáo toán học: " Permutation Patterns and Continued Fractions" pptx

Báo cáo toán học: " Permutation Patterns and Continued Fractions" pptx

... generating function for the number of (132)-avoiding permutations that have a given number of (123) patterns, and show how to extend this to permutations that have exactly one (132) pattern. We ... numerator and denominator. First, from (3) we have that P (q, z, t)= 1 1−zP(q,zt, tq) , (5) the electronic journal of combinatorics 6 (1999), #R38 6 Finally, to find the denominator...
Ngày tải lên : 07/08/2014, 06:20
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Báo cáo toán học: "CALCUL BASIQUE DES PERMUTATIONS SIGNEES, II: ANALOGUES FINIS DES FONCTIONS DE BESSEL" pps

Báo cáo toán học: "CALCUL BASIQUE DES PERMUTATIONS SIGNEES, II: ANALOGUES FINIS DES FONCTIONS DE BESSEL" pps

... Combinatorics on words. — Reading, Addison-Wesley,  (Encyclop edia of Math. and its Appl., 17). [Mac13] MacMahon (Percy Alexander). — The indices of permutations and the derivation therefrom of ... de toutes les multipermutations sign´ees, en r´eduisant le nombre des variables. Ceci fait l’objet du paragraphe suivant. 9. Fonction g´en´eratrice de toutes les multipermutations sign´ee...
Ngày tải lên : 07/08/2014, 06:22
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Báo cáo toán học: "Combinatorial Identities from the Spectral Theory of Quantum Graph" potx

Báo cáo toán học: "Combinatorial Identities from the Spectral Theory of Quantum Graph" potx

... Systems, and by a grant from the Israel Science Foundation. We thank Uri Gavish for introducing us to the combinatorial literature, and Brendan McKay and Herbert Wilf for their interest and support. ... indebted to Gregory Berkolaiko for his idea concerning the proof of (7) and (8), and to Akalu Tefera for his kind help in obtaining a computer-aided proof of (2). Reference...
Ngày tải lên : 07/08/2014, 06:23
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Báo cáo toán học: "321-polygon-avoiding permutations and Chebyshev polynomials" pps

Báo cáo toán học: "321-polygon-avoiding permutations and Chebyshev polynomials" pps

... Mansour and A. Vainshtein, Layered restrictions and Chebychev polynomials (2000), Annals of Combinatorics 5 (2001) 451–458. [MV4] T. Mansour and A. Vainshtein, Restricted permutations and Chebyshev ... West, and G. Xin, Wilf–equivalence for singelton classes, in Proc. 13th Conf. in Formal Power Series and Algebraic Combinatorics, Tempe 2001. [Bo1] M. B´ona, The permutation class...
Ngày tải lên : 07/08/2014, 07:21
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Báo cáo toán học: "Counting 1324-avoiding Permutations" docx

Báo cáo toán học: "Counting 1324-avoiding Permutations" docx

... 1324-avoiding permutations for length up to 20 Definition 5. Two permutations π and σ are said to be in the same strong class if the left -to right minima of π are the same as those of σ andtheyoccurinthesameposition; and ... n,then k + 1 has to be the second entry of σ ;and2 )ifk + 1 occurs to the right of a 1 =1,then k + 1 has to be the next -to- last entry of σ. Hence, 13...
Ngày tải lên : 07/08/2014, 07:21
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Báo cáo toán học: "Pattern avoidance in permutations: linear and cyclic orders" pdf

Báo cáo toán học: "Pattern avoidance in permutations: linear and cyclic orders" pdf

... a 1 <a 2 and a 3 <a 4 (note that s 3 and s 4 belong to the same horizontal edge); since there are at least two long horizontal edges and s 2 and s 3 belong respectively to the first and last ... µ −1 ν p and n = kp. We need to calculate how many operators reduce to each one of the four scenarios in (4.9). Clearly λ =1⇔ µ = ν, so a non-trivial operator will reduce t...
Ngày tải lên : 07/08/2014, 07:21
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Báo cáo toán học: "Packing patterns into words" pptx

Báo cáo toán học: "Packing patterns into words" pptx

... d(Π,σ(Π,k,n)) = δ(Π,k,n). To find δ(Π), we will need to find δ(Π,k,n), hence maximal Π-containing permutations σ(Π,k,n) are of interest to us, especially, their asymptotic shape as n → and k →∞. Example ... packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns...
Ngày tải lên : 07/08/2014, 07:21
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