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A list of arithmetical structures complete with respect to the first-order definability

Theoretical Computer Science, ISSN 0304-3975, 2001, Volume 257, Issue 1, pp. 115 - 151

... if the operations +,× are definable in it. A list of such structures is presented. Although structures with Pascal's triangles modulo n are preferred a little, an effort was made to collect...

Arithmetical structures | Pascal's triangle modulo [formula omitted] | Elementary definability | Undecidable theories | Pascal's triangle modulo n | AUTOMATA | elementary definability | PASCAL TRIANGLES | MODULO | UNDECIDABLE EXTENSIONS | DECIDABILITY | DIVISIBILITY | COPRIMENESS PREDICATE | INTEGERS | SUCCESSOR FUNCTION | undecidable theories | COMPUTER SCIENCE, THEORY & METHODS | PRIMES | Pascal's triangle module n | arithmetical structures

Arithmetical structures | Pascal's triangle modulo [formula omitted] | Elementary definability | Undecidable theories | Pascal's triangle modulo n | AUTOMATA | elementary definability | PASCAL TRIANGLES | MODULO | UNDECIDABLE EXTENSIONS | DECIDABILITY | DIVISIBILITY | COPRIMENESS PREDICATE | INTEGERS | SUCCESSOR FUNCTION | undecidable theories | COMPUTER SCIENCE, THEORY & METHODS | PRIMES | Pascal's triangle module n | arithmetical structures

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

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

Pascal's triangle modulo n | Decidability | Definability | MATHEMATICS | decidability | definability | SETS | PREDICATE | PRIMES | Pascal's triangle module n

Journal Article

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

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

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

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

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

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

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

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

Fibonacci diagonal | modular arithmetic | Pascal matrix | Modular arithmetic | MATHEMATICS

Journal Article

Acta Cybernetica, ISSN 0324-721X, 2018, Volume 23, Issue 3

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 1/2016, Volume 55, Issue 1, pp. 203 - 227

In Sturmfels and Whiteley (J Symb Comput 11(5):439–453, 1991), it is proven that any multihomogenous bracket polynomial with integer coefficients can be...

Grassmann–Cayley algebra | 15A75 | Computational Mathematics and Numerical Analysis | 15A72 | Cayley factorization | Ruler constructions | Bracket polynomials | 51A05 | Projectively invariant properties | Mathematics | Combinatorics | MATHEMATICS | THEOREMS | Grassmann-Cayley algebra | COMPUTER SCIENCE, THEORY & METHODS | INVARIANT-THEORY | GEOMETRY | Algebra | Algorithms | Geometry | Polynomials | Pascal (programming language) | Construction | Brackets | Constants | Factorization | Invariants

Grassmann–Cayley algebra | 15A75 | Computational Mathematics and Numerical Analysis | 15A72 | Cayley factorization | Ruler constructions | Bracket polynomials | 51A05 | Projectively invariant properties | Mathematics | Combinatorics | MATHEMATICS | THEOREMS | Grassmann-Cayley algebra | COMPUTER SCIENCE, THEORY & METHODS | INVARIANT-THEORY | GEOMETRY | Algebra | Algorithms | Geometry | Polynomials | Pascal (programming language) | Construction | Brackets | Constants | Factorization | Invariants

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

High-level graphics language | Portable software | Pascal | Minicomputer system | Computer graphics

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