Related papers: Dyck tilings of type $D$
Dyck paths (also balanced brackets and Dyck words) are among the most heavily studied Catalan families. This paper is a continuation of [2, 3, 4]. In the paper we are dealing with the numbering of Dyck paths, with the resulting numbers, the…
We continue to investigate applications of $k$-covers in function spaces with the compact-open topology.
In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we…
In this article we introduce a simple dynamical system called symplectic billiards. As opposed to usual/Birkhoff billiards, where length is the generating function, for symplectic billiards symplectic area is the generating function. We…
We give a group-theoretic description of the parity of a pull-back of a theta characteristic under a branched covering. It involves lifting monodromy of the covering to the semidirect product of the symmetric and Clifford groups, known as…
It is well-known that the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the Yangian in type $A$ yields generators of its Drinfeld presentation. Defining relations between these generators are known in an…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
This paper proposes a fully-automatic, text-guided generative method for producing perfectly-repeating, periodic, tile-able 2D imagery, such as the one seen on floors, mosaics, ceramics, and the work of M.C. Escher. In contrast to square…
We study generating functions in the context of Rota-Baxter algebras. We show that exponential generating functions can be naturally viewed in a very special case of complete free commutative Rota-Baxter algebras. This allows us to use free…
This is a noncommutative-geometric study of the semiclassical dynamics of finite topological D-brane systems. Starting from the formulation in terms of A -infinity categories, I show that such systems can be described by the noncommutative…
This work answers the question what coverings over a topological torus can be induced from a covering over a space of dimension $k$. The answer to this question is then applied in algebro-geometric context to present obstructions to…
In a recent paper we proposed the study of aggregation functions on lattices via clone theory approach. Observing that aggregation functions on lattices just correspond to $0,1$-monotone clones, we have shown that all aggregation functions…
A generative model is developed for deep (multi-layered) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up (pretraining) and top-down (refinement)…
We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior…
Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for…
In this paper we describe explicit generating functions for a large class of Hurwitz-Hodge integrals. These are integrals of tautological classes on moduli spaces of admissible covers, a (stackily) smooth compactification of the Hurwitz…
This paper studies silted algebras, namely, endomorphism algebras of 2-term silting complexes, over path algebras of Dynkin quivers. We will describe an algorithm to produce all basic 2-term silting complexes over the path algebra of a…
We revisit our earlier work which lead to a periodic table of Borcherds-Kac-Moody algebras that appeared in the context of the refined generating function of quarter-BPS (dyons) in $\mathcal{N}=4$ supersymmetric four-dimensional string…
An infinite class of $4d$ $\mathcal{N}=1$ gauge theories can be engineered on the worldvolume of D3-branes probing toric Calabi-Yau 3-folds. This kind of setup has multiple applications, ranging from the gauge/gravity correspondence to…
Bipolar orientations of planar maps have recently attracted some interest in combinatorics, probability theory and theoretical physics. Plane bipolar orientations with $n$ edges are known to be counted by the $n$th Baxter number $b(n)$,…