Zobrazeno 1 - 10
of 43
pro vyhledávání: '"05A16, 05A15"'
Autor:
Greenwood, Torin, Larson, Tristan
We derive asymptotic formulae for the coefficients of bivariate generating functions with algebraic and logarithmic factors. Logarithms appear when encoding cycles of combinatorial objects, and also implicitly when objects can be broken into indecomp
Externí odkaz:
http://arxiv.org/abs/2405.08133
We call a pair of vertex-disjoint, induced subtrees of a rooted trees twins if they have the same counts of vertices by out-degrees. The likely maximum size of twins in a uniformly random, rooted Cayley tree of size $n\to\infty$ is studied. It is sho
Externí odkaz:
http://arxiv.org/abs/2312.01190
In the context of lattice walk enumeration in cones, we consider the number of walks in the quarter plane with fixed starting and ending points, prescribed step-set and given length. After renormalization, this number may be interpreted as a discrete
Externí odkaz:
http://arxiv.org/abs/2309.15209
Autor:
Nessmann, Andreas
Enumeration of walks with small steps in the quadrant has been a topic of great interest in combinatorics over the last few years. In this article, it is shown how to compute exact asymptotics of the number of such walks with fixed start- and endpoin
Externí odkaz:
http://arxiv.org/abs/2307.11539
Autor:
Rastegar, Reza
We offer elementary proofs for several results in consecutive pattern containment that were previously demonstrated using ideas from cluster method and analytical combinatorics. Furthermore, we establish new general bounds on the growth rates of cons
Externí odkaz:
http://arxiv.org/abs/2304.14733
Autor:
Monteil, Thierry, Nurligareev, Khaydar
We compute the whole asymptotic expansion of the probability that a large uniform labeled graph is connected, and of the probability that a large uniform labeled tournament is irreducible. In both cases, we provide a combinatorial interpretation of t
Externí odkaz:
http://arxiv.org/abs/2205.06487
We establish the asymptotic normality of the dimension of large-size random Fishburn matrices by a complex-analytic approach. The corresponding dual problem of size distribution under large dimension is also addressed and follows a quadratic type nor
Externí odkaz:
http://arxiv.org/abs/2012.13570
Autor:
Zhou, Nian Hong
Publikováno v:
Bulletin of the Australian Mathematical Society (2020)
In this paper, we investigate $\pi(m,n)$, the number of partitions of the \emph{bipartite number} $(m,n)$ into \emph{steadily decreasing} parts, introduced by L.Carlitz ['A problem in partitions', Duke Math Journal 30 (1963), 203--213]. We give a rel
Externí odkaz:
http://arxiv.org/abs/1909.07762
Publikováno v:
29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), Leibniz International Proceedings in Informatics (LIPIcs), vol 110
Non-negative {\L}ukasiewicz paths are special two-dimensional lattice paths never passing below their starting altitude which have only one single special type of down step. They are well-known and -studied combinatorial objects, in particular due to
Externí odkaz:
http://arxiv.org/abs/1801.02996
Publikováno v:
Theoretical Computer Science 705 (2018), pp. 31-57
The register function (or Horton-Strahler number) of a binary tree is a well-known combinatorial parameter. We study a reduction procedure for binary trees which offers a new interpretation for the register function as the maximal number of reduction
Externí odkaz:
http://arxiv.org/abs/1612.07286