Related papers: A skeleton model to enumerate standard puzzle sequ…
We introduce a large family of combinatorial objects, called standard puzzles, defined by very simple rules. We focus on the standard puzzles for which the enumeration problems can be solved by explicit formulas or by classical numbers,…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
We introduce a density-based clustering method called skeleton clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density…
We introduce a combinatorial enumeration problem that is solved using generalized Catalan numbers. We also study generalizations of the Cycle Lemma beyond the computation of the generalized Catalan numbers.
Narrative story generation is a challenging problem because it demands the generated sentences with tight semantic connections, which has not been well studied by most existing generative models. To address this problem, we propose a…
We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solubility of some equations and distribution of sequences in small intervals. We obtain classic and…
Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Edge-to-trail substitution…
A skeleton representation of the human body has been proven to be effective for this task. The skeletons are presented in graphs form-like. However, the topology of a graph is not structured like Euclidean-based data. Therefore, a new set…
Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9 \times 9$ square with numbers 1 through 9,…
Recent advances in the joint processing of images have certainly shown its advantages over individual processing. Different from the existing works geared towards co-segmentation or co-localization, in this paper, we explore a new joint…
Skeletonization has been a popular shape analysis technique that models both the interior and exterior of an object. Existing template-based calculations of skeletal models from anatomical structures are a time-consuming manual process.…
Skeletonization is a popular shape analysis technique that models an object's interior as opposed to just its boundary. Fitting template-based skeletal models is a time-consuming process requiring much manual parameter tuning. Recently,…
Modeling coherence in text has been a task that has excited NLP researchers since a long time. It has applications in detecting incoherent structures and helping the author fix them. There has been recent work in using neural networks to…
Appearance features have been widely used in video anomaly detection even though they contain complex entangled factors. We propose a new method to model the normal patterns of human movements in surveillance video for anomaly detection…
We describe arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects specified as a Haskell type class. Our algorithms work on a {\em generic} representation that we illustrate on…
Motivated by representation theory we exhibit an interior structure to Catalan sequences and many generalisations thereof. Certain of these coincide with well known (but heretofore isolated) structures. The remainder are new.
The notion of a mesh pattern was introduced recently, but it has already proved to be a useful tool for description purposes related to sets of permutations. In this paper we study eight mesh patterns of small lengths. In particular, we…
We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…
In this paper we determine the parity of some sequences which are related to Catalan numbers. Also we introduce a combinatorical object called, \Catalan tree", and discuss its properties.
Symmetric functions provide one of the most efficient tools for combinatorial enumeration, in the context of objects that may be acted upon by permutations. Only assuming a basic knowledge of linear algebra, we introduce and describe the…