The on-line encyclopedia of integer sequences
TLDR
The On-Line Encyclopedia of Integer Sequences (OEIS) as mentioned in this paper is a database of some 130000 number sequences, which is freely available on the Web (http://wwwresearchattcom/~njas/sequences/) and is widely used.Abstract:
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences It is freely available on the Web (http://wwwresearchattcom/~njas/sequences/) and is widely used
There are several ways in which it benefits research: 1 It serves as a dictionary, to tell the user what is known about a particular sequence There are hundreds of papers which thank the OEIS for assistance in this way
1 The associated Sequence Fans mailing list is a worldwide network which has evolved into a powerful machine for tackling new problems
1 As a direct source of new theorems, when a sequence arises in two different contexts
1 As a source of new research, when one sees a sequence in the OEIS that cries out to be analyzed
The 40-year history of the OEIS recapitulates the story of modern computing, from punched cards to the internet
The talk will be illustrated with numerous examples, emphasizing new sequences that have arrived in the past few months Many open problems will be mentioned
Because of the profusion of books and journals, volunteers play an important role in maintaining the database If you come across an interesting number sequence in a book, journal or web site, please send it and the reference to the OEIS (You do not need to be the author of the sequence to do this) There is a web site for sending in "Comments" or "New sequences"
Several new features have been added to the OEIS in the past year Thanks to the work of Russ Cox, searches are now performed at high speed, and thanks to the work of Debby Swayne, there is a button which displays plots of each sequence Finally, a "listen" button enables one to hear the sequence played on a musical instrument (try Recamaan's sequence A005132!)read more
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Journal ArticleDOI
Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay
TL;DR: The models indicate that both the dishonest and the honest miners were worse off than they would have been if no dishonest mining were present, and that it is possible for the mining community to detect block-hiding behaviour, such as that used in selfish-mine, by monitoring the rate of production of orphan blocks.
Journal ArticleDOI
Multiloop Functional Renormalization Group That Sums Up All Parquet Diagrams.
Fabian B. Kugler,Jan von Delft +1 more
TL;DR: It is shown that solving the multiloop FRG flow is equivalent to solving the (first-order) parquet equations and illustrated this with numerical results.
Posted Content
The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron
TL;DR: In this paper, the T-duality map is used to obtain a dissection of the amplituhedron from a dissections of the hypersimplex and vice-versa.
Posted Content
Some Fundamental Theorems in Mathematics
Abstract: An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 135 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [5] without leading to panic. The order is not a ranking but more like a time-line when things were written down. Since [280] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context” we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The number of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable” theorems with proofs included. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [110, 106, 20, 137, 312, 215, 78], for history [124, 316, 193, 40, 30, 116, 195, 188, 347, 63, 311, 43, 140, 174], for popular, beautiful or elegant things [8, 267, 113, 101, 13, 338, 339, 28, 107, 133, 229, 309, 113, 1, 70, 85, 71, 255]. For comprehensive overviews in large parts of mathematics, [41, 93, 94, 32, 297] or predictions on developments [31]. For reflections about mathematics in general [84, 233, 29, 163, 227, 56, 284]. Encyclopedic source examples are [105, 352, 336, 57, 109, 88, 126, 108, 61, 319].
Journal ArticleDOI
Properties and Constructions of Constrained Codes for DNA-Based Data Storage
TL;DR: Property and constructions of constraint-based codes for DNA-based data storage which account for the maximum repetition length and AT/GC balance and routines for translating binary runlength limited and/or balanced strings into DNA strands are described.