相关论文: Three Generalizations of Davenport-Schinzel Sequen…

We study the longest increasing subsequence problem for random permutations avoiding the pattern $312$ and another pattern $\tau$ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average…

Neural ordinary differential equations (neural ODEs) are a popular family of continuous-depth deep learning models. In this work, we consider a large family of parameterized ODEs with continuous-in-time parameters, which include…

We introduce a generalization of the zig-zag product of regular digraphs (directed graphs), which allows us to construct regular digraphs with m ore flexible choices of the degrees. In our generalization, we can control the connectivity of…

Maximal green sequences are particular sequences of quiver mutations appearing in the context of quantum dilogarithm identities and supersymmetric gauge theory. Interpreting maximal green sequences as paths in various natural posets arising…

We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…

The expressiveness of deep neural network (DNN) is a perspective to understandthe surprising performance of DNN. The number of linear regions, i.e. pieces thata piece-wise-linear function represented by a DNN, is generally used to…

We obtain a sharp bound on the number of self-intersections of a closed planar curve with trigonometric parameterization. Moreover, we show that a generic curve of this form is normal in the sense of Whitney.

The sequence a_1,...,a_m is a common subsequence in the set of permutations S = {p_1,...,p_k} on [n] if it is a subsequence of p_i(1),...,p_i(n) and p_j(1),...,p_j(n) for some distinct p_i, p_j in S. Recently, Beame and Huynh-Ngoc (2008)…

In this paper we derive new upper bounds for the densities of measurable sets in R^n which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new…

We provide a completely new relation between curvature bounds and definiteness of the causal character of maximizers by exploiting the robust notion of synthetic curvature. This enables us to relate low-regularity inextendibility of…

This letter presents a direct construction of cross Z-complementary sequence sets (CZCSSs), whose aperiodic correlation sums exhibit zero correlation zones at both the front-end and tail-end shifts. CZCSS can be regarded as an extension of…

The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…

We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, $O(N)$-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin…

Permutons, which are probability measures on the unit square $[0, 1]^2$ with uniform marginals, are the natural scaling limits for sequences of (random) permutations. We introduce a $d$-dimensional generalization of these measures for all…

We develop a flexible technique to bound the characters of symmetric groups, via the Naruse hook length formula, the Larsen--Shalev character bounds, and appropriate diagram slicings. It allows us to prove a uniform exponential character…

A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences…

We obtain sharp upper bounds for three-term segments of a bounded power series. Along the way we show that the Taylor polynomials of a certain algebraic function do not vanish in the unit disk.

A generalization of the Davenport constant is investigated. For a finite abelian group $G$ and a positive integer $k$, let $D_k(G)$ denote the smallest $\ell$ such that each sequence over $G$ of length at least $\ell$ has $k$ disjoint…

In this paper, we bring the terminology of the Kunz coordinates of numerical semigroups to gapsets and we generalize this concept to $m$-extensions. It allows us to identify gapsets and, in general, $m$-extensions with tilings of boards. As…

Understanding bounds for the effective differential Nullstellensatz is a central problem in differential algebraic geometry. Recently, several bounds have been obtained using Dicksonian and antichains sequences (with a given growth rate).…