A Continuous Analogue of Lattice Path Enumeration
نویسندگان
چکیده
منابع مشابه
Lattice path enumeration and Toeplitz matrices
This paper is about counting lattice paths. Examples are the paths counted by Catalan, Motzkin or Schröder numbers. We identify lattice paths with walks on some path-like graph. The entries of the nth power of the adjacency matrix are the number of paths of length nwith prescribed start and end position. The adjacency matrices turn out to be Toeplitz matrices. Explicit expressions for eigenvalu...
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If f = EW:-, a,,t” is a formal Laurent series with certain restrictions on the a,, then f = f-fof+ , where fcontains only negative powers of t, f+ contains only positive powers of t, and f. is independent of t. Applications include Lagrange’s formula for series reversion, the problem of counting lattice paths below a diagonal, and a theorem of Furstenberg that the diagonal of a rational power s...
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The Goulden–Jackson cluster method is a powerful tool for obtaining generating functions for counting words in a free monoid by occurrences of a set of subwords. We introduce a generalization of the cluster method for monoid networks, which generalize the combinatorial framework of free monoids. As a sample application of the generalized cluster method, we compute bivariate and multivariate gen...
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The cluster representation matrices have already been successfully used to enumerate close-packed vacancy clusters in all single-lattice crystals [I, 2]. Point defect clusters in double-lattice crystals may have identical geometry but are distinct due to unique atomic postions enclosing them. The method of representation matrices is extended to make it applicable to represent and enumerate ...
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the cluster representation matrices have already been successfully used to enumerate close-packed vacancy clusters in all single-lattice crystals [i, 2]. point defect clusters in double-lattice crystals may have identical geometry but are distinct due to unique atomic postions enclosing them. the method of representation matrices is extended to make it applicable to represent and enumerate the ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8788