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The initial segmentation phase is crucial in image processing to simplify the image representation and extract some desired features. Different methods and techniques have been proposed for image multi-level thresholding, but they are still stuck ...

We illustrate the power of symbolic computation and experimental mathematics by investigating maximal seating arrangements, either on a line, or in a rectangular auditorium with a fixed number of columns but an arbitrary number of rows, that obey ...

Finite difference discretization of the two-dimensional space-fractional diffusion equations derives a complicated linear system consisting of identity matrix and four scaled block-Toeplitz with Toeplitz block (BTTB) matrices resulted from the ...

A bijection is given between the set of directed column-convex polyominoes on triangular and honeycomb lattices of area n and some families of restricted compositions. This is an analogous result to one given by Deutsch and Prodinger for ...

We introduce L m-Motzkin paths similar to m-Dyck paths. For fixed positive integer m, L m-Motzkin paths are a generalization of Motzkin paths that start at ( 0 , 0 ), use steps U = ( 1 , 1 ), D = ( 1 , − 1 ) and L = ( 1 , 0 ), remain weakly above ...

Suppose that a 0 , a 1 , … is an integer sequence which satisfies a recurrence relation with constant coefficients, and let T ( x ) = f ( x ) / g ( x ) be its generating function, where f ( x ) and g ( x ) have no common factors in Z [ x ]. In ...

We define the p , q-Legendre-Stirling numbers P S p , q ( n , k ) of the second kind, which reduce to the Legendre-Stirling numbers P S ( n , k ) of the second kind discovered by Everitt, Littlejohn and Wellman when p = 1 and q = 1 and the q-...

Based on the finite-difference method, the considered Riesz space-fractional diffusion equations result in a series of linear systems, whose coefficient matrices are composed of the identity matrix and the product of diagonal matrix and Toeplitz ...$\mathrm{}$$$

An adjacent q-cycle is a natural generalization of an adjacent transposition. We show that the number of adjacent q-cycles in a permutation maps to the sum of occurrences of two mesh patterns under Foata's fundamental transformation. As a ...

A simple and easy-to-implement discrete approximation is proposed for one-dimensional higher-order integral fractional Laplacian (IFL), and our method is applied to discrete the fractional biharmonic equation, multi-term fractional differential ...

A multiple leaf-distance granular regular α-tree (abbreviated as LDR α-tree for short) is a tree (with at least α + 1 vertices) where any two leaves are at some distance divisible by α. A connected graph's subtree which is additionally an LDR α-...

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as ...

• We give a combinatorial explanation of the weighted enumeration of rooted spanning forests of a graph.
• We give a combinatorial explanation of the characteristic polynomial of a graph.
• We give a combinatorial explanation of the ...

Assume that G is a graph with n vertices v 1 , v 2 , … , v n. Given a rooted spanning forest F of G, which has s components and roots v k 1 , v k 2 , … , v k s, define the weight ω ( F ) of F to be ∏ i = 1 s x k i, where x 1 , x 2 , … , x n are n ...

Persistence modules and barcodes are used in symplectic topology to define various invariants of Hamiltonian diffeomorphisms, however numerical methods for computing these barcodes are not yet well developed. In this paper we define one such ...${\mathbb{}}^{\mathrm{}}$

Queueing systems with vacations have been used in various applications, such as cellular networks and sensor networks, where base station sleeping is an effective way to improve the energy-efficiency of the network (it corresponds to a power-...

We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the x-axis are enumerated by the generalized Catalan numbers, and we give a constructive ...

Let A be an infinite sequence of positive integers and let m = { ( k 1 , m 1 ) , ⋯ , ( k l , m l ) } be a set of integer tuples such that gcd ⁡ ( m 1 , m 2 , ⋯ , m l ) > 1. Denote by R m ( A , n ) the number of different solutions of the equation ...

Let I n denote the set of inversion sequences of length n. In this paper, we enumerate members of I n represented using positive integers according to parameters which track the number of runs and successions of letters of a given ...

Consider a card guessing game with complete feedback in which a deck of n cards ordered 1 , … , n is riffle-shuffled once. With the goal to maximize the number of correct guesses, a player guesses cards from the top of the deck one at ...

It is known that the following five counting problems lead to the same integer sequence $f_t(n)$:

1. the number of nonequivalent compact Huffman codes of length n over an alphabet of t letters,
2. the number of “nonequivalent” complete rooted t-ary trees (...