Corpus ID: 236469444

Injectively $k$-colored rooted forests

@inproceedings{Einolf2021InjectivelyR,
  title={Injectively \$k\$-colored rooted forests},
  author={Thomas Einolf and Robert Muth and J. C. Wilkinson},
  year={2021}
}
We enumerate injectively k-colored rooted forests with a given number of vertices of each color and a given sequence of root colors. We obtain from this result some new multi-parameter distributions of Fuss-Catalan numbers. As an additional application we enumerate triangulations of regular convex polygons according to their proper 3-coloring type. 

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SHOWING 1-10 OF 29 REFERENCES
Obstructions to Injective Oriented Colourings
TLDR
Efficient algorithms are described, based on colouring extension, which produce either the desired colouring or a forbidden substructure when the number of colours is at most three. Expand
Injective Oriented Colourings
TLDR
The theory of oriented colourings which are injective on in-neighbourhoods are developed, and a linear algorithm that decides if a given tree can be coloured with at most k colours, where k is fixed, is described. Expand
On the injective chromatic number of graphs
TLDR
The injective chromatic number of the hypercube is explored in particular and its context is put in the context of previous work on similar concepts, especially the theory of error-correcting codes. Expand
A study on the injective coloring parameters of certain graphs
TLDR
The concepts of mean and variance are extended to a modified injective graph coloring and the values of these parameters for a number of standard graphs are determined. Expand
Injective coloring of planar graphs
TLDR
It is proved that if G is a planar graph with girth g and maximum degree @D, then @g"i(G)@?@D=@D if either g>=20 and @D>=3, or g >=7 and @ D>=71, and the injective chromatic number@g" i (G) is the least k such that there is an injective k-coloring. Expand
Good and Semi-Strong Colorings of Oriented Planar Graphs
TLDR
It is shown that every oriented planar graph G = (V,A) with d-(x) ⩽ 3 for every x ϵ V has a good and semi-strong coloring using at most 4 x 5 x 24 colors. Expand
Catalan Numbers
Sequences and arrays whose terms enumerate combinatorial structures have many applications in computer science. Knowledge (or estimation) of such integer-valued functions is, for example, needed inExpand
The Raney numbers and (s, s+1)-core partitions
TLDR
A recurrence relation is obtained for the Raney numbers which is a generalization of the recurrencerelation for the Catalan numbers which confirms a conjecture posed by Amdeberhan concerning the enumeration of $\lambda$-core partitions with parts that are multiples of $p. Expand
Some identities for the Catalan and Fine numbers
We establish combinatorial interpretations of several identities for the Catalan and Fine numbers and, along the way, we present some new bijections of independent interest. Briefly, we show thatExpand
Ordered trees with prescribed root degrees, node degrees, and branch lengths
A new decomposition of ordered trees is introduced. It turns out to be very convenient for finding multivariate generating functions according to branch related statistics. Same decomposition is usedExpand
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