相关论文: Integer sequences and matrices over finite fields
This article gives a brief introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms…
In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.
An introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS, https://oeis.org) for graduate students in mathematics
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…
In this paper, we study the Euler-Seidel matrices with coefficients and determine the associated Riordan matrix to a given matrix, if it does exist. Computation of the generating fonction of the final sequence is established by the…
This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of…
Stephan (Prove or Disprove 100 Conjectures from the OES, arXiv:math/0409509v4 [math.CO])enumerates a number of conjectures regarding integer sequences contained in Sloane's On-line Encyclopedia of Integer Sequences (N. J. A. Sloane, editor,…
The first author recently introduced an integer sequence now numbered A355519 in OEIS. This sequence arose from counting bracket tournaments; its study evokes the analysis of the Catalan triangle (sequence A009766 in OEIS) and the related…
Let $\beta$ be any permutation on $n$ symbols and let $c(k, \beta)$ be the number of permutations that $k$-commute with $\beta$. The cycle type of a permutation $\beta$ is a vector $(c_1, \dots, c_n)$ such that $\beta$ has exactly $c_i$…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.
We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…
Infinite sequences are of tremendous theoretical and practical importance, and in the Information Age sequences of 0s and 1s are of particular interest. Over the past century, the field of symbolic dynamics has developed to study sequences…
The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that most combinatorialists, and many other mathematicians and scientists, use at least once a day, is a treasure trove of mathematical information, and, one of its…
In this paper 101 new integer sequences, sub-sequences, and sequences of sequences, together with related unsolved problems and conjectures, are presented. Also, definitions, examples, solved or open questions, and references for each…
The On-Line Encyclopedia of Integer Sequences (OEIS) is a web-accessible database cataloging interesting integer sequences and associated theorems. With more than 12,000 citations, the OEIS is one of the most highly cited resources in all…