منابع مشابه
Counting Lattice Paths
Counting lattice paths Maciej Dziemiańczuk A lattice path is a finite sequence of points p0, p1, . . . , pn in Z × Z, and a step of the path is the difference between two of its consecutive points, i.e., pi−pi−1. In this thesis, we consider lattice paths running between two fixed points and for which the set of allowable steps contains the vertical step (0,−1) and some number (possibly infinite...
متن کاملCounting Paths in Young’s Lattice
Young’s lattice is the lattice of partitions of integers, ordered by inclusion of diagrams. Standard Young tableaux can be represented as paths in Young’s lattice that go up by one square at each step, and more general paths in Young’s lattice correspond to more general kinds of tableaux. Using the theory of symmetric functions, in particular Pieri’s rule for multiplying a Schur function by a c...
متن کاملSQUARE q , t - LATTICE PATHS AND ∇ ( p n ) NICHOLAS
The combinatorial q, t-Catalan numbers are weighted sums of Dyck paths introduced by J. Haglund and studied extensively by Haglund, Haiman, Garsia, Loehr, and others. The q, t-Catalan numbers, besides having many subtle combinatorial properties, are intimately connected to symmetric functions, algebraic geometry, and Macdonald polynomials. In particular, the n’th q, t-Catalan number is the Hilb...
متن کاملSQUARE q , t - LATTICE PATHS AND ∇ ( p n ) NICHOLAS A
The combinatorial q, t-Catalan numbers are weighted sums of Dyck paths introduced by J. Haglund and studied extensively by Haglund, Haiman, Garsia, Loehr, and others. The q, t-Catalan numbers, besides having many subtle combinatorial properties, are intimately connected to symmetric functions, algebraic geometry, and Macdonald polynomials. In particular, the n’th q, t-Catalan number is the Hilb...
متن کاملSQUARE q , t - LATTICE PATHS AND ∇ ( p n )
The combinatorial q, t-Catalan numbers are weighted sums of Dyck paths introduced by J. Haglund and studied extensively by Haglund, Haiman, Garsia, Loehr, and others. The q, t-Catalan numbers, besides having many subtle combinatorial properties, are intimately connected to symmetric functions, algebraic geometry, and Macdonald polynomials. In particular, the n’th q, t-Catalan number is the Hilb...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1982
ISSN: 0097-3165
DOI: 10.1016/0097-3165(82)90002-4