Combinatorial Enumeration

By Ian P. Goulden, D. M. Jackson. 2004

797 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/33f4b91b8c23b075393f3441ff1f03283e66938e

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Citations in the corpus

A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees (2011, methodology): “The exact values for all even n ≤ 24 are available as Sequence A002829 in Sloane’s wonderful On-Line Encyclopedia of Integer Sequences [66], and in general they can be computed using a messy recurrence in Goulden and Jackson [32].”
Analytic Combinatorics (2009, methodology): “Many examples are to be found in Goulden and Jac kson’s book [303].”
THE FERMAT CUBIC, ELLIPTIC FUNCTIONS, CONTINUED FRACTIONS, AND A COMBINATORIAL EXCURSION (2005, unknown): “tation diﬀers. Indeed, one may think of the Fran¸con–Viennot correspondence given in [27] as the gradual construction of an increasing binary tree, upon successively appending nodes at dangling links [19, 30]; see also Figure 12, where both a snake and the underlying tree are represented. Use will m”
Riordan group involutions (2008, methodology): “In Section 2, we give a useful characterization of a Riordan matrix in terms of the Stieltjes transform [5,7].”
KP hierarchy for Hodge integrals (2008, background): “The fact that these changes of variables are inverse to one another follows from the Lagrange inversion theorem, see [7,9].”
Counting Walks in the Quarter Plane (2017, methodology): “The formulation we use here is different both from Brown’s original presentation and from the one in Goulden and Jackson’s book [23].”
The enumeration of simple permutations. (2003, methodology): “We will apply inclusion-exclusion arguments (dressed in the form of generating functions [5, 6]), an argument which allows us to reduce the number of terms considered, and a bootstrapping approach.”
The KP hierarchy, branched covers, and triangulations (2008, background): “, [4]; interestingly, Hurwitz seems to have been the first person to write this down clearly), we have B = log(B̃) (20)”
Logarithmic Combinatorial Structures: A Probabilistic Approach (2003, unknown): “For further treatment of the algebraic aspects of decomposable structures, the reader is referred to Foata (1974) and Joyal (1981) and to the books by Goulden and Jackson (1983), Stanley (1986) and Bergeron, Labelle and Leroux (1997).”
Lagrange Inversion: When and How (2007, background): “, [6]), and we can summarize its most relevant aspects in the following three points which can overlap each other:”