Results 41 to 50 of about 20,234 (200)
Automatic Classification of Restricted Lattice Walks [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We propose an $\textit{experimental mathematics approach}$ leading to the computer-driven $\textit{discovery}$ of various conjectures about structural properties of generating functions coming from enumeration of restricted lattice walks in 2D and in 3D.
Alin Bostan, Manuel Kauers
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Talmudic lattice path counting
Journal of Combinatorial Theory, Series A, 1994 Consider all planar walks, with positive unit steps (1,0) and (0,1) from the origin (0,0) to a given point \((a,b)\). Let \(L\) be the line joining the beginning to the end. For \(i= 0,1,\dots, a+ b-1\), let \(W_ i\) be the set of walks with ``exactly'' \(i\) points above and ``exactly'' \(a+ b+ 1- i\) points below \(L\).
Jane Friedman +2 more
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Further Rogers-Ramanujan type identities for modified lattice paths
, 2023 Recently, the authors introduced the modified lattice paths which generalize Agarwal-Bressoud weighted lattice paths. Using these new objects they interpreted combinatorially two basic series identities which led to two new combinatorial Rogers-Ramanujan
Ashok Kumar Agarwal, Sachdeva, Rachna
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$n$-color overpartitions, lattice paths, and multiple basic hypergeometric series [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We define two classes of multiple basic hypergeometric series $V_{k,t}(a,q)$ and $W_{k,t}(a,q)$ which generalize multiple series studied by Agarwal, Andrews, and Bressoud.
Olivier Mallet
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Bijections of dominant regions in the $m$-Shi arrangements of type $A$, $B$ and $C$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 In the present paper, the relation between the dominant regions in the $m$-Shi arrangement of types $B_n/C_n$, and those of the $m$-Shi arrangement of type $A_{n-1}$ is investigated. More precisely, it is shown explicitly how the sets $R^m(B_n)$ and $R^m(
Myrto Kallipoliti, Eleni Tzanaki
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Deformations of Weyl's Denominator Formula [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a series of conjectured identities that deform Weyl's denominator formula and generalize Tokuyama's formula to other root systems. These conjectures generalize a number of well-known results due to Okada.
Angêle Hamel, Ronald King
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Scientific Reports, 2023 The femtosecond time-resolved impulsive stimulated Raman scattering (fs-ISRS) has been performed to study the low frequency lattice mode dynamics of the RDX crystal.
Guoyang Yu +5 more
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A Combinatorial Bijection between Ordered Trees and Lattice Paths
Trends in Computational and Applied Mathematics, 2023 This work presents a combinatorial bijection between the set of lattice paths and the set of ordered trees, both counted by the central coefficients of the expansion of the trinomial (1+x+x^2)^n. Moreover, using a combinatorial interpretation of Catalan
L. Rocha, E. V. Pereira Spreafico
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Paired Patterns in Lattice Paths [PDF]
, 2019 Let $\mathcal{L}_n$ denote the set of all paths from $[0,0]$ to $[n, n]$ which consist of either unit north steps $N$ or unit east steps $E$ or, equivalently, the set of all words $L \in \{E,N\}^*$ with $n$ $E$'s and $n$ $N$'s. Given $L \in \mathcal{L}_n$ and a subset $A$ of $[n] = \{1, \ldots, n\}$, we let $ps_{L}(A)$ denote the word that results from
Pan, Ran, Remmel, Jeffrey B.
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A Bijection for Directed-Convex Polyominoes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we consider two classes of lattice paths on the plane which use \textitnorth, \textiteast, \textitsouth,and \textitwest unitary steps, beginningand ending at (0,0).We enumerate them according to the number ofsteps by means of bijective ...
Alberto Del Lungo +3 more
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