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Theoretical Computer Science, ISSN 0304-3975, 2001, Volume 257, Issue 1, pp. 115 - 151
Journal Article
2009, ISBN 9780195334548, xiv, 422
Like the intriguing Fibonacci and Lucas numbers, Catalan numbers are also ubiquitous. "They have the same delightful propensity for popping up unexpectedly,... 
Catalan numbers (Mathematics) | Mathematics | Euler's triangulation problem | Pascal's triangle | Pascal's identity | Lucas numbers | Catalan sequence | Parenthesization problem | Catalan numbers | Martin gardner | Fibonacci numbers
Book
Fundamenta Mathematicae, ISSN 0016-2736, 1998, Volume 156, Issue 2, pp. 111 - 129
Let Sq denote the set of squares, and let SQ(n) be the squaring function restricted to powers of n... 
Pascal's triangle modulo n | Decidability | Definability | MATHEMATICS | decidability | definability | SETS | PREDICATE | PRIMES | Pascal's triangle module n
Journal Article
by Bes, A
ANNALS OF PURE AND APPLIED LOGIC, ISSN 0168-0072, 12/1997, Volume 89, Issue 1, pp. 17 - 35
In the first part of the paper we study arithmetical properties of Pascal triangles module a prime power... 
MATHEMATICS | MATHEMATICS, APPLIED | decidability | definability | LUCAS | Pascal's triangle module n
Journal Article
Acta Arithmetica, ISSN 0065-1036, 2017, Volume 181, Issue 1, pp. 27 - 55
... in the $n$-th row of Pascal's triangle that are exactly divisible by $p^j$. Moreover, for a finite sequence $w=(w_{r-1}\cdots w_0)\neq (0,\ldots,0)$ in $\{0,\ldots,p-1\}$ we denote by $\lvert n\rvert_w... 
MATHEMATICS | NUMBER | generating functions | FIXED POWER | DIGITAL SUMS | CONGRUENCE | binomial coefficients modulo powers of primes | exact enumeration | DIVIDES | PASCAL TRIANGLE
Journal Article
Asian Journal of Mathematics, ISSN 1093-6106, 2018, Volume 22, Issue 1, pp. 41 - 74
...) with certain constraints. For the representation ring r(K Z(n)/J(d)), we completely determine its generators and the relations of generators via the method of the Pascal triangle... 
Shift ring | Monoidal category | Nakayama truncated algebra | Pascal triangle | Derived representation ring | Representation ring | MATHEMATICS | MATHEMATICS, APPLIED | shift ring | HOPF-ALGEBRAS | derived representation ring | GREEN RINGS | monoidal category
Journal Article
Discrete Mathematics and Theoretical Computer Science, ISSN 1462-7264, 2010, Volume 12, Issue 3, pp. 1 - 28
M.-P. Schutzenberger asked to determine the support of the free Lie algebra L-Zm (A) on a finite alphabet A over the ring Z(m) of integers mod m and all pairs... 
Free Lie algebras | λ-Tabloids | Pascal triangle mod m | Shuffle product | Set partitions | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | SHUFFLE ALGEBRA | set partitions | shuffle product | lambda-tabloids | Computer Science | Discrete Mathematics
Journal Article
1999, 1st ed., ISBN 1565923987, xvii, 684
Book
Journal of Mathematical Modelling and Algorithms, ISSN 1570-1166, 3/2010, Volume 9, Issue 1, pp. 53 - 97
An original algorithm is presented that generates both restricted integer compositions and restricted integer partitions that can be constrained simultaneously... 
Integer partitions | Bounded partitions | 11P82 | Pascal’s triangle | Numeric Computing | Integer compositions | Mathematics | Optimization | Algorithms | 11Y55 | 11Y16 | Bounded compositions | Operations Research, Mathematical Programming | Mathematical Modeling and Industrial Mathematics | Fibonacci | 05A07 | Pascal's triangle | Integer programming | Studies | Mathematical analysis
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 12/1998, Volume 125, Issue 4, pp. 269 - 278
Denote byx a random infinite path in the graph of Pascal's triangle (left and right turns are selected independently with fixed probabilities) and byd n (x... 
Pascal adic transformation | 28D99 | weak mixing | measure preserving transformation | 28D05 | Uniform distribution modulo 1 | Mathematics, general | Mathematics | eigenvalue | Eigenvalue | Weak mixing | Measure preserving transformation | MATHEMATICS | uniform distribution modulo 1
Journal Article
Logic Journal of IGPL, ISSN 1367-0751, 8/2007, Volume 15, Issue 4, pp. 313 - 320
In the School of Mathematical Sciences at Queen Mary in the University of London we have been running a module that teaches the students to write good mathematical English... 
Discharging assumptions | Mathematical exposition | Definition | Writing | Informal logic | Logic | Pascal | Natural deduction | discharging assumptions | MATHEMATICS | mathematical exposition | natural deduction | MATHEMATICS, APPLIED | informal logic | writing | definition | logic
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 04/2000, Volume 47, Issue 2, pp. 129 - 136
Let B denote either of two varieties of order n Pascal matrix, i.e., one whose entries are the binomial coefficients... 
Fibonacci diagonal | modular arithmetic | Pascal matrix | Modular arithmetic | MATHEMATICS
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 1/2016, Volume 55, Issue 1, pp. 203 - 227
Journal Article
Proceedings of the 1978 annual conference, 01/1978, Volume 2, pp. 704 - 712
PIGLI (Portable Interactive Graphics Language Interpreter) is a high-level interactive graphics system implemented on an INTERDATA 8/32 minicomputer. PIGLI is... 
High-level graphics language | Portable software | Pascal | Minicomputer system | Computer graphics
Conference Proceeding
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