Results 41 to 50 of about 90 (78)
Some formulas for the restricted r-Lah numbers [PDF]
, 2018 The r-Lah numbers, which we denote here by `(r)(n, k), enumerate partitions of an (n+r)-element set into k+r contents-ordered blocks in which the smallest r elements belong to distinct blocks. In this paper, we consider a restricted version `(r) m (n,
Shattuck, Mark
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Some collapsibility results for n-dimensional contingency tables
Collapsibility, Conditional independence, Contingency table, Log-linear model, Möbius inversion, Simpson’s paradox, Strict collapsibility, Primary 62H17, Secondary 62E99, Secondary 05A05,
P. Vellaisamy, V. Vijay
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The graham–knuth–patashnik recurrence: symmetries and continued fractions
, 2022 72 pags. -- Mathematics Subject Classifications: 05A10 (Primary); 05A15, 05A19, 30B70 (Secondary)We study the triangular array defined by the Graham–Knuth–Patashnik recurrence T (n, k) = (αn + βk + γ) T (n − 1, k) + (αn + βk + γ ) T (n − 1, k − 1) with ...
Sokal, Alan D., Salas, Jesús
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Boolean elements in the Bruhat order [PDF]
We show that a Weyl group element is boolean if and only if it avoids a set of Billey-Postnikov patterns, which we describe explicitly. Our proof is based on analysis of inversion sets, and it is in large part type-uniform.
Gao, Yibo, Hänni, Kaarel
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The derivation of cycle index of Sn[3]
, 2004 WE evaluate the cycle index polynomial of the reduced triple group Sn[3]. We also use similar techniques to derive the cycle index polynomial of the triple group Sn(3) which had earlier been found by Oberschelp (see Palmer [8] who has also given an ...
Kamuti, IN, Obon’go, JO
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Slit-slide-sew bijections for oriented planar maps
We construct growth bijections for bipolar oriented planar maps and for Schnyder woods. These give direct combinatorial proofs of several counting identities for these objects. Our method mainly uses two ingredients.
Éric Fusy +2 more
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Melham's conjecture on odd power sums of fibonacci numbers
, 2016 Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at a certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish
Xie, Matthew H.Y. +2 more
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Invariant cubature formulae for spheres and balls by combinatorial methods
, 2008 . Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp.
Sangwoo Heo, Yuan Xu
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Skeletal generalizations of chip-firing games, parking functions, and Dyck paths
For \(0\leq k\leq n-1\), we introduce a family of \(k\)-skeletal paths which are counted by the \(n\)th Catalan number for each \(k\), and specialize to Dyck paths when \(k=n-1\).
Backman, Spencer +5 more
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Математическо моделиране при дизайна на тъкачни структури
, 2010 Красимир Йорджев, Христина Костадинова - В работата се разглежда една релация на еквивалентност в множеството от всички квадратни бинарни матрици. Обсъдена е комбинаторната задача за намиране мощността и елементите на фактормножеството относно тази ...
Kostadinova, Hristina +1 more
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