Related papers: Generating trees growing on the left for pattern-a…
A perceptron that learns the opposite of its own output is used to generate a time series. We analyse properties of the weight vector and the generated sequence, like the cycle length and the probability distribution of generated sequences.…
We recover Gessel's determinantal formula for the generating function of permutations with no ascending subsequence of length m+1. The starting point of our proof is the recursive construction of these permutations by insertion of the…
Counterfactuals can explain classification decisions of neural networks in a human interpretable way. We propose a simple but effective method to generate such counterfactuals. More specifically, we perform a suitable diffeomorphic…
We propose generating functions which encode the degeneracies and wall-crossing phenomena of $\mathcal{N}=2$ BPS structures. The generating functions have a representation-theoretic origin and are the analogs of the 1/4-BPS dyon counting…
We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends…
We find the generating function for the class of all permutations that avoid the patterns 3124 and 4312 by showing that it is an inflation of the union of two geometric grid classes.
Extracting a Construction Tree from potentially noisy point clouds is an important aspect of Reverse Engineering tasks in Computer Aided Design. Solutions based on algorithmic geometry impose constraints on usable model representations…
Counterfactuals have become a popular technique nowadays for interacting with black-box machine learning models and understanding how to change a particular instance to obtain a desired outcome from the model. However, most existing…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
We give the generating function for the index of integer lattice points, relative to a finite order ideal. The index is an important concept in the theory of border bases, an alternative to Gr\"obner bases. Equivalently, we explicitly solve…
We give an improved algorithm for counting the number of $1324$-avoiding permutations, resulting in $14$ further terms of the generating function, which is now known for all patterns of length $\le 50$. We re-analyse the generating function…
For every sufficiently well-behaved function $g:\mathbb{R}_{\ge 0}\rightarrow\mathbb{R}_{\ge 0}$ that grows at least linearly and at most exponentially we construct a tree $T$ of uniform volume growth $g$, that is, $$C_1\cdot g(r/4)\le…
It is known that a tilting generator on an algebraic variety $X$ gives a derived equivalence between $X$ and a certain non-commutative algebra. In this paper, we explain a method to construct a tilting generator from an ample line bundle,…
The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…
Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. R{\'e}my showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary…
We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted…
We consider the problem of enumerating spanning trees on lattices. Closed-form expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N_1 x N_2 x...x N_d in d dimensions under free, periodic, and…
We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weights along the individual edges. We give two…
In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the…
Generation and prediction of time series is analyzed for the case of a Bit-Generator: a perceptron where in each time step the input units are shifted one bit to the right with the state of the leftmost input unit set equal to the output…