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11: 26.2 Basic Definitions
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Lattice Path
►A lattice path is a directed path on the plane integer lattice . …For an example see Figure 26.9.2. ►A k-dimensional lattice path is a directed path composed of segments that connect vertices in so that each segment increases one coordinate by exactly one unit. … ►12: 26.3 Lattice Paths: Binomial Coefficients
§26.3 Lattice Paths: Binomial Coefficients
►§26.3(i) Definitions
… ► is the number of lattice paths from to . …The number of lattice paths from to , , that stay on or above the line is … ► …13: 26.5 Lattice Paths: Catalan Numbers
§26.5 Lattice Paths: Catalan Numbers
►§26.5(i) Definitions
… ►It counts the number of lattice paths from to that stay on or above the line . … ► …14: 26.6 Other Lattice Path Numbers
§26.6 Other Lattice Path Numbers
… ►Delannoy Number
… ►Motzkin Number
… ►Narayana Number
… ►Schröder Number
…15: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
§26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
►§26.4(i) Definitions
… ►It is also the number of -dimensional lattice paths from to . … ► …16: 26.9 Integer Partitions: Restricted Number and Part Size
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►It follows that also equals the number of partitions of into parts that are less than or equal to .
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►It is also equal to the number of lattice paths from to that have exactly vertices , , , above and to the left of the lattice path.
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17: 20 Theta Functions
Chapter 20 Theta Functions
…18: 31.6 Path-Multiplicative Solutions
§31.6 Path-Multiplicative Solutions
►A further extension of the notation (31.4.1) and (31.4.3) is given by …These solutions are called path-multiplicative. …19: 31.18 Methods of Computation
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►Care needs to be taken to choose integration paths in such a way that the wanted solution is growing in magnitude along the path at least as rapidly as all other solutions (§3.7(ii)).
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20: 8 Incomplete Gamma and Related
Functions
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