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Abstract: 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 NN f(0; 0)g, where N denotes the nonnegative integers. We give a bijective proof of the identity e(n) = 2 n 1 d(n) for n 1. In giving perspective for our proof, we consider bijections between sets of lattice paths defined on various sets of permitted steps which yield path counts related to the Narayana... (Update)
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.... the number of elements in the corresponding cell) The unweighted forms of such paths (or trivial variations) are enumerated in [14] and [13] the former of which also provides a bijective interpretation of the relationship between their enumeration and that of...
...x k ; y k )g. Then (x 1 ; y 1 ) x h ) x n k ; y n k ) are the left turns of the path F (P ) 2 A (n) This was mistyped in [21]. where fx 1 ; x n k g = f1; ng fx 1 ; x k g fy 1 ; y n k g = f0; n 1g fy 1 ;...
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BibTeX entry: (Update)
Robert A. Sulanke. Counting lattice paths by Narayana polynomials. Electron. J. Combin., 7(1):Research Paper 40, 9 pp. (electronic), 2000. 16 http://citeseer.ist.psu.edu/sulanke00counting.html More
@misc{ sulanke00counting,
author = "R. Sulanke",
title = "Counting lattice paths by Narayana polynomials",
text = "Robert A. Sulanke. Counting lattice paths by Narayana polynomials. Electron.
J. Combin., 7(1):Research Paper 40, 9 pp. (electronic), 2000. 16",
year = "2000",
url = "citeseer.ist.psu.edu/sulanke00counting.html" }
Citations (may not include all citations):267 Enumerative Combinatorics (context) - Stanley - 1999
6 oder numbers arising from combinatorial statistics on lattic.. (context) - Bonin, Shapiro et al. - 1993
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