Related papers: A multivariate "inv" hook formula for forests
Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous…
We extend a classical construction on symmetric functions, the superization process, to several combinatorial Hopf algebras, and obtain analogs of the hook-content formula for the (q,t)-specializations of various bases. Exploiting the…
We take an elementary approach to derive a generalization of Kunth's formula using Lassalle's explicit formula. In particular, we give a formula for the Kostka numbers of a shape $\mu\vdash n$ and weight $(m,1^{n-m})$ for $m=3,\;4$.
We study configuration space integral formulas for Milnor's homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. Our proof is essentially a combinatorial analysis of a…
Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this…
We consider a multivariate distributional recursion of sum-type as arising in the probabilistic analysis of algorithms and random trees. We prove an upper tail bound for the solution using Chernoff's bounding technique by estimating the…
The last decade has witnessed a growing interest in random forest models which are recognized to exhibit good practical performance, especially in high-dimensional settings. On the theoretical side, however, their predictive power remains…
We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange-Good inversion formula, which has other applications such as counting coloured trees or studying probability generating…
We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such that the Free Uniform Spanning Forest in the direct product of the k-regular tree and H has infinitely many trees almost surely.…
A planar tree power series over a field $K$ is a formal expression $$\sum c_T \cdot T$$ where the sum is extended over all isomorphism classes of finite planar reduced rooted trees $T$ and where the coefficients $c_T$ are in $K$.…
We study Coxeter racks over $\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are…
We show that any convergent (shuffle) arborified zeta value admits a series representation. This justifies the introduction of a new generalisation to rooted forests of multiple zeta values, and we study its algebraic properties. As a…
Hajek's stochastic comparison result is generalised to multivariate stochastic sum processes with univariate convex data functions and for univariate monoton nondecreasing convex data functions for processes with and without drift…
We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural…
We study spanning diverging forests of a digraph and related matrices. It is shown that the normalized matrix of out forests of a digraph coincides with the transition matrix in a specific observation model for Markov chains related to the…
We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…
Let $A$ be a commutative $k$-algebra over a field of $k$ and $\Xi$ a linear operator defined on $A$. We define a family of $A$-valued invariants $\Psi$ for finite rooted forests by a recurrent algorithm using the operator $\Xi$ and show…
In this series of papers, we propose a theory of enumerative invariants counting self-dual objects in self-dual categories. Ordinary enumerative invariants in abelian categories can be seen as invariants for the structure group $\mathrm{GL}…
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…