Results 81 to 90 of about 20,234 (200)
, 2023 A lattice path in $\Z^d$ is a sequence $\nu_1,\nu_2,\ldots,\nu_k\in\Z^d$ such that the steps $\nu_i-\nu_{i-1}$ lie in a subset $\S$ of $\Z^d$ for all $i=2,\ldots,k$. Let $T_{m,n}$ be the $m\times n$ table in the first area of the $xy$-axis and put $\S=\{(
Ghasemian Zoeram, Hamed +2 more
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Type C parking functions and a zeta map [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We introduce type $C$ parking functions, encoded as vertically labelled lattice paths and endowed with a statistic dinv'. We define a bijection from type $C$ parking functions to regions of the Shi arrangement of type $C$, encoded as diagonally labelled ...
Robin Sulzgruber, Marko Thiel
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Trapezoidal lattice paths and multivariate analogues
, 2003 In 1996, Garsia and Haiman introduced a bivariate analogue of the Catalan numbers that counts multiplicities of the sign character in a certain doubly graded Sn-module.
Loehr, N.
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Counting Pairs of Lattice Paths by Intersections
Journal of Combinatorial Theory, Series A, 1996 On an $r\times (n-r)$ lattice rectangle, we first consider walks that begin at the SW corner, proceed with unit steps in either of the directions E or N, and terminate at the NE corner of the rectangle. For each integer $k$ we ask for $N_k^{n,r}$, the number of {\em ordered\/} pairs of these walks that intersect in exactly $k$ points.
Ira M. Gessel +4 more
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A Continuous Analogue of Lattice Path Enumeration
The Electronic Journal of Combinatorics, 2019 Following the work of Cano and Díaz, we consider a continuous analog of lattice path enumeration. This process allows us to define a continuous version of many discrete objects that count certain types of lattice paths. As an example of this process, we define continuous versions of binomial and multinomial coefficients, and describe some identities ...
Quang Nhat Le +3 more
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Partitions with constrained ranks and lattice paths [PDF]
Enumerative Combinatorics and Applications, 2023 Sylvie Corteel +2 more
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Lattice paths and n-colour compositions
, 2008 Extending the ‘walks’ of van Lint and Wilson, we introduce a new kind of weighted lattice paths and show that the number of lattice paths with weight ν+m-1(0⩽m⩽ν-1) equals the number of n-colour compositions of ν.
Narang, Geetika, Agarwal, A.K.
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Algorithms, 2015 We propose a linear time algorithm, called G2DLP, for generating 2D lattice L(n1, n2) paths, equivalent to two-item multiset permutations, with a given number of turns.
Ting Kuo
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Symmetric Subsets of Lattice Paths
, 2000 Let [n] = {0, 1,...,n}. A subset S of [n] is symmetric if S = g − S for a natural number g. We show that, for every f : [n] → [2n] with the restriction 1 ≤ f(i + 1) − f(i) ≤ 2 for all i<n, there is some S ⊂ [n] such that |S| ≥ 2 ln n − O(1), with the property that both S and f(S) are symmetric.
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Counting Lattice Paths by Narayana Polynomials [PDF]
The Electronic Journal of Combinatorics, 2000 Let $d(n)$ count the lattice paths from $(0,0)$ to $(n,n)$ using the steps (0,1), (1,0), and (1,1). Let $e(n)$ count the lattice paths from $(0,0)$ to $(n,n)$ with permitted steps from the step set ${\bf N} \times {\bf N} - \{(0,0)\}$, where ${\bf N}$ denotes the nonnegative integers. We give a bijective proof of the identity $e(n) = 2^{n-1} d(
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