منابع مشابه
Enumeration of digraph embeddings
A cellular embedding of an Eulerian digraph D into a closed surface is said to be directed if the boundary of each face is a directed closed walk in D. The directed genus polynomial of an Eulerian digraph D is the polynomial ΓD(x) = ∑ h≥0 gh(D)x h where gh(D) is the number of directed embeddings into the orientable surface Sh, of genus h, for h = 0, 1, . . . . The sequence {gh(D)|h ≥ 0}, which ...
متن کاملGeneralized Catalan numbers and the enumeration of planar embeddings
The Raney numbers Rp,r(k) are a two-parameter generalization of the Catalan numbers that were introduced by Raney in his investigation of functional composition patterns. We give a new combinatorial interpretation for the Raney numbers in terms of planar embeddings of certain collections of trees, a construction that recovers the usual interpretation of the p-Catalan numbers in terms of p-ary t...
متن کاملRegular embeddings of complete bipartite graphs: classification and enumeration
The regular embeddings of complete bipartite graphs Kn,n in orientable surfaces are classified 5 and enumerated, and their automorphism groups and combinatorial properties are determined. The method depends on earlier classifications in the cases where n is a prime power, obtained in collaboration with Du, Kwak, Nedela and Škoviera, together with results of Itô, Hall, Huppert and Wielandt on fa...
متن کاملEnumeration of Increasing Boolean Expressions and Alternative Digraph Implementations for Diagnostic Applications
In classification and diagnostic applications, items are categorized according to observations of item attributes. A classification scheme specifies which observations are made, and in what order. The classification scheme determines how, after each observation, an item is either assigned to a category, or subjected to another observation. In real systems, observations have cost, and miscategor...
متن کاملDigraph Decompositions and Monotonicity in Digraph Searching
We consider monotonicity problems for graph searching games. Variants of these games – defined by the type of moves allowed for the players – have been found to be closely connected to graph decompositions and associated width measures such as pathor tree-width. Of particular interest is the question whether these games are monotone, i.e. whether the cops can catch a robber without ever allowin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2014
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.10.003