Book ChapterDOI
Combinatorial Mathematics: THE PRINCIPLE OF INCLUSION AND EXCLUSION
About:
The article was published on 1963-01-01. It has received 150 citations till now.read more
Citations
More filters
Book
Discriminants, Resultants, and Multidimensional Determinants
TL;DR: The Cayley method of studying discriminants was used by Cayley as discussed by the authors to study the Cayley Method of Discriminants and Resultants for Polynomials in One Variable and for forms in Several Variables.
Journal ArticleDOI
Boson Sampling on a Photonic Chip
Justin B. Spring,Benjamin J. Metcalf,Peter C. Humphreys,W. Steven Kolthammer,Xian-Min Jin,Xian-Min Jin,Marco Barbieri,Aanimesh Datta,Nicholas Thomas-Peter,Nathan K. Langford,Nathan K. Langford,Dmytro Kundys,James C. Gates,Brian J. Smith,Pete Smith,Ian A. Walmsley +15 more
TL;DR: A quantum boson-sampling machine (QBSM) is constructed to sample the output distribution resulting from the nonclassical interference of photons in an integrated photonic circuit, a problem thought to be exponentially hard to solve classically.
Journal ArticleDOI
Split graphs
TL;DR: The main topics of this article are split graphs, their degree sequences, and the place of these "split partitions" at the top of the partially ordered set of graphic partitions.
Proceedings ArticleDOI
Finding, minimizing, and counting weighted subgraphs
TL;DR: These algorithms rely on fast algorithms for computing the permanent of a k x n matrix, over rings and semirings and give a new (algorithmic) application of multiparty communication complexity.
Journal ArticleDOI
On Artin's conjecture and Euclid's algorithm in global fields
TL;DR: In this paper, the authors considered a generalization of Artin's conjecture on primes with prescribed primitive roots and provided a necessary and sufficient condition for the conjectural density of certain sets of primes to be non-zero.
References
More filters
Book
Discriminants, Resultants, and Multidimensional Determinants
TL;DR: The Cayley method of studying discriminants was used by Cayley as discussed by the authors to study the Cayley Method of Discriminants and Resultants for Polynomials in One Variable and for forms in Several Variables.
Journal ArticleDOI
Boson Sampling on a Photonic Chip
Justin B. Spring,Benjamin J. Metcalf,Peter C. Humphreys,W. Steven Kolthammer,Xian-Min Jin,Xian-Min Jin,Marco Barbieri,Aanimesh Datta,Nicholas Thomas-Peter,Nathan K. Langford,Nathan K. Langford,Dmytro Kundys,James C. Gates,Brian J. Smith,Pete Smith,Ian A. Walmsley +15 more
TL;DR: A quantum boson-sampling machine (QBSM) is constructed to sample the output distribution resulting from the nonclassical interference of photons in an integrated photonic circuit, a problem thought to be exponentially hard to solve classically.
Journal ArticleDOI
Split graphs
TL;DR: The main topics of this article are split graphs, their degree sequences, and the place of these "split partitions" at the top of the partially ordered set of graphic partitions.
Proceedings ArticleDOI
Finding, minimizing, and counting weighted subgraphs
TL;DR: These algorithms rely on fast algorithms for computing the permanent of a k x n matrix, over rings and semirings and give a new (algorithmic) application of multiparty communication complexity.
Journal ArticleDOI
On Artin's conjecture and Euclid's algorithm in global fields
TL;DR: In this paper, the authors considered a generalization of Artin's conjecture on primes with prescribed primitive roots and provided a necessary and sufficient condition for the conjectural density of certain sets of primes to be non-zero.