Suppose that we are given two independent sets Ib and Ir of a graph such that |Ib| = |Ir|, and imagine that a token is placed on each vertex in Ib. Then, the sliding token problem is to determine whether there exists a sequence of independent sets which transforms Ib into Ir so that each independent set in the sequence results from the previous one by sliding exactly one token along an edge in ...

Abstract. The Kauffman-Vogel polynomial is an invariant of unoriented four-valent graphs embedded in three dimensional space. In this article we give a one variable generalization of this invariant. This generalization is given as a sequence of invariants in which the first term is the Kauffman-Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group repres...

In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and search terms k-generalized Fibonacci sequence which repdigits. particular, find numbers powers 10 special case second part by using roots characteristic polynomial sequence, introduce tiny golden angles show feasibility new type in application to magnetic res...

We introduce a fast algorithm for determining the linear complexity and the minimal polynomial of a sequence with period p over GF(q) , where p is an odd prime, q is a prime and a primitive root modulo p; and its two generalized algorithms. One is the algorithm for determining the linear complexity and the minimal polynomial of a sequence with period pq over GF(q), the other is the algorithm fo...

We answer an open question in the theory of degrees of infinite sequences with respect to transducibility by finite-state transducers. An initial study of this partial order of degrees was carried out in [5], but many basic questions remain unanswered. One of the central questions concerns the existence of atom degrees, other than the degree of the ‘identity sequence’ 10101010 · · · . A degree ...

An infinite bit sequence is called recursively random if no computable strategy betting along the sequence has unbounded capital. It is wellknown that the property of recursive randomness is closed under computable permutations. We investigate analogous statements for randomness notions defined by betting strategies that are computable within resource bounds. Suppose that S is a polynomial time...

We characterize the polynomial closure of a pseudo-convergent sequence in valuation domain V arbitrary rank, and then we use this result to show that is never topological when has rank at least 2.

In this paper, we propose primitive rateless (PR) codes. A PR code is characterized by the message length and a polynomial over $\mathbf{GF}(2)$, which can generate potentially limitless number of coded symbols. We show that codewords truncated at any arbitrary be represented as subsequences maximum-length sequence ($m$-sequence). characterize Hamming weight distribution codes their duals for p...

In a non-cooperative context, receiver has to estimate the communication parameters without any prior knowledge of transmitter, which is highly demanding. Estimating self-synchronous scrambler even more challenging because scrambling sequence affected by input sequence. This paper proposes an improved algorithm for blind estimation using orthogonal property bias condition received signals in di...

In this paper, we study the desingularization problem in the first qWeyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that s...