Results 1  10
of
1,334,554
PATTERN AVOIDANCE
"... Consider a sequence of letters or numbers. Does a pattern exist that is avoided by the sequence? This topic is a very popular area of research in mathematics for its promising utility in computer science and other branches of mathematics, the elegant proofs and solutions, ..."
Abstract
 Add to MetaCart
Consider a sequence of letters or numbers. Does a pattern exist that is avoided by the sequence? This topic is a very popular area of research in mathematics for its promising utility in computer science and other branches of mathematics, the elegant proofs and solutions,
Generalized pattern avoidance
 European J. Combin
"... Abstract. Recently, Babson and Steingrímsson have introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We will consider pattern avoidance for such patterns, and give a complete solution for the number of pe ..."
Abstract

Cited by 86 (5 self)
 Add to MetaCart
Abstract. Recently, Babson and Steingrímsson have introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We will consider pattern avoidance for such patterns, and give a complete solution for the number
PATTERN AVOIDANCE IN LABELLED TREES
 SÉMINAIRE LOTHARINGIEN DE COMBINATOIRE 67 (2012), ARTICLE B67B
, 2012
"... We discuss a new notion of pattern avoidance motivated by operad theory: pattern avoidance in planar labelled trees. It is a generalisationofvarioustypesofconsecutivepattern avoidancestudiedbefore: consecutivepatternsinwords,permutations, colouredpermutations,etc. ThenotionofWilfequivalenceforpatter ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We discuss a new notion of pattern avoidance motivated by operad theory: pattern avoidance in planar labelled trees. It is a generalisationofvarioustypesofconsecutivepattern avoidancestudiedbefore: consecutivepatternsinwords,permutations, colouredpermutations,etc. Thenotionof
Pattern avoidance classes and subpermutations
, 2004
"... Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers a structure theorem is given. The structure theorem shows th ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers a structure theorem is given. The structure theorem shows
Pattern avoidance in ascent sequences
 Electron. J. Combin
"... Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to (2+2)free posets and various other combinatorial structures. We study pattern avoidanc ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
avoidance in ascent sequences, giving several results for patterns of lengths up to 4, for Wilf equivalence and for growth rates. We establish bijective connections between pattern avoiding ascent sequences and various other combinatorial objects, in particular with set partitions. We also make a number
Pattern avoidance in binary trees
 J. Combin. Theory, Ser. A
"... Abstract. This paper introduces the notion of pattern avoidance in binary trees. We provide an algorithm for computing the generating function that counts the number of nleaf binary trees avoiding a given binary tree pattern t. Equipped with this counting mechanism, we study the analogue of Wilf eq ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
Abstract. This paper introduces the notion of pattern avoidance in binary trees. We provide an algorithm for computing the generating function that counts the number of nleaf binary trees avoiding a given binary tree pattern t. Equipped with this counting mechanism, we study the analogue of Wilf
Statistics on patternavoiding permutations
, 2004
"... This thesis concerns the enumeration of patternavoiding permutations with respect to certain statistics. Our first result is that the joint distribution of the pair of statistics ‘number of fixed points’ and ‘number of excedances’ is the same in 321avoiding as in 132avoiding permutations. This ge ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
This thesis concerns the enumeration of patternavoiding permutations with respect to certain statistics. Our first result is that the joint distribution of the pair of statistics ‘number of fixed points’ and ‘number of excedances’ is the same in 321avoiding as in 132avoiding permutations
Pattern Avoidance in the Rook Monoid
, 2014
"... We consider two types of pattern avoidance in the rook monoid, i.e. the set of 0–1 square matrices with at most one nonzero entry in each row and each column. For onedimensional rook patterns, we completely characterize monoid elements avoiding a single pattern of length at most three and develop a ..."
Abstract
 Add to MetaCart
We consider two types of pattern avoidance in the rook monoid, i.e. the set of 0–1 square matrices with at most one nonzero entry in each row and each column. For onedimensional rook patterns, we completely characterize monoid elements avoiding a single pattern of length at most three and develop
Pattern Avoidance in Ternary Trees
"... This paper considers the enumeration of ternary trees (i.e., rooted ordered trees in which each vertex has 0 or 3 children) avoiding a contiguous ternary tree pattern. We begin by finding recurrence relations for several simple tree patterns; then, for more complex trees, we compute generating funct ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
This paper considers the enumeration of ternary trees (i.e., rooted ordered trees in which each vertex has 0 or 3 children) avoiding a contiguous ternary tree pattern. We begin by finding recurrence relations for several simple tree patterns; then, for more complex trees, we compute generating
Results 1  10
of
1,334,554