Combinatorial Gray Codes

Joichi, J. T.; White, Dennis E.; Williamson, S. Gill

doi:10.1137/0209013

Cited by 42 publications

(24 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By definition, a Gray code for a combinatorial family is a listing of objects in the family such that successive objects differ in some prespecified, usually small, way [2]. In [9] a Gray code list for the set of Fibonacci strings defined by (1) …”

Section: Gray Code For S N (T P )mentioning

confidence: 99%

See 1 more Smart Citation

Combinatorial isomorphism between Fibonacci classes

Juarna¹,

Vajnovszki

2008

Journal of Discrete Mathematical Sciences and Cryptography

View full text Add to dashboard Cite

In 1985 Simion and Schmidt showed that the set S n (T 3 ) of length n permutations avoiding the set of patterns T 3 = {123, 132, 213} is counted by (the second order) Fibonacci numbers. They also presented a constructive bijection between the set F n−1 of length (n − 1) binary strings with no two consecutive 1s and S n (T 3 ).In 2005, Egge and Mansour generalized the first Simion-Simion's result and showed that S n (T p ), the set of permutations avoiding the patterns T p = {12 . . . p, 132, 213}, is counted by the (p − 1)th order Fibonacci numbers.In this paper we extend the second Simion-Schmidt's result by giving a bijection between the set F (p−1) n−1 of length (n − 1) binary strings with no (p − 1) consecutive 1s, and the set S n (T p ). Moreover, we show that this bijection is a combinatorial isomorphism, i.e., a closeness-preserving bijection, by which we transform a known Gray code (or equivalently Hamiltonian path) and exhaustive generating algorithm for F (p−1) n−1 into similar results for S n (T p ).

show abstract

Section: Gray Code For S N (T P )mentioning

confidence: 99%

“…(2) For each n ≥ 1, the following is a constructive bijection between F (2) n−1 and the set S n (T 3 ) of binary strings of length (n − 1) having no two consecutive ones: Let b = b 1 b 2 . .…”

Section: Introductionmentioning

confidence: 99%

Combinatorial isomorphism between Fibonacci classes

Juarna¹,

Vajnovszki

2008

Journal of Discrete Mathematical Sciences and Cryptography

View full text Add to dashboard Cite

show abstract

“…Roughly speaking, a Gray code is a listing of the objects in a combinatorial family so that successive objects differ 'in some pre-specified small way' [5]. Here we adhere to the definition given in [14]: a Gray code for a combinatorial family is a listing of the objects in the family so that successive objects differ by a number of changes bounded independently of the object-size.…”

Section: Introductionmentioning

confidence: 98%

Restricted compositions and permutations: From old to new Gray codes

Vajnovszki

Vernay

2011

Information Processing Letters

View full text Add to dashboard Cite

“…A very special way for listing a class of combinatorial objects is the so called combinatorial Gray code, where two consecutive objects differ 'in some pre-specified small way' [7]. In [17] a general definition is given, where a Gray code is defined as 'an infinite set of word-lists with unbounded word-length such that the Hamming distance between any two adjacent words is bounded independently of the word-length' (the Hamming distance is the number of positions in which the words differ).…”

Section: Introductionmentioning

confidence: 99%

Gray code orders for $$q$$ q -ary words avoiding a given factor

et al. 2015

View full text Add to dashboard Cite

Based on BRGC inspired order relations we define Gray codes and give a generating algorithm for q-ary words avoiding a prescribed factor. These generalize an early 2001 result and a very recent one published by some of the present authors, and can be seen as an alternative to those of Squire published in 1996. Among the involved tools, we make use of generalized BRGC order relations, ultimate periodicity of infinite words, and word matching techniques.

show abstract

Combinatorial Gray Codes

Cited by 42 publications

References 6 publications

Combinatorial isomorphism between Fibonacci classes

Combinatorial isomorphism between Fibonacci classes

Restricted compositions and permutations: From old to new Gray codes

Gray code orders for $$q$$ q -ary words avoiding a given factor

Contact Info

Product

Resources

About