Zobrazeno 1 - 10
of 145
pro vyhledávání: '"ATKINSON, M. D."'
A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate than non-deflatable ones. Some theorems which guarantee non-deflatabi
Externí odkaz:
http://arxiv.org/abs/1409.5296
Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure, including their
Externí odkaz:
http://arxiv.org/abs/1308.3262
We enumerate three specific permutation classes defined by two forbidden patterns of length four. The techniques involve inflations of geometric grid classes.
Externí odkaz:
http://arxiv.org/abs/1209.0425
The structure of three pattern classes Av(2143, 4321), Av(2143, 4312) and Av(1324, 4312) is determined using the machinery of monotone grid classes. This allows the permutations in these classes to be described in terms of simple diagrams and regular
Externí odkaz:
http://arxiv.org/abs/1206.3183
Autor:
Albert, Michael, Atkinson, M. D.
When a set of permutations comprising a pattern class C is submitted as input to a priority queue the resulting output is again a pattern class C'. The basis of C' is determined for pattern classes C whose basis elements have length 3, and is finite
Externí odkaz:
http://arxiv.org/abs/1202.1542
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods, we prove th
Externí odkaz:
http://arxiv.org/abs/1108.6319
We enumerate the pattern class Av(2143,4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes.
Externí odkaz:
http://arxiv.org/abs/1108.0989
A poset is {\it $(\3+\1)$-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the
Externí odkaz:
http://arxiv.org/abs/1102.5568
Let B be the operation of re-ordering a sequence by one pass of bubble sort. We completely answer the question of when the inverse image of a principal pattern class under B is a pattern class.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/1008.5299
We prove that all subclasses of the separable permutations not containing Av(231) or a symmetry of this class have rational generating functions. Our principal tools are partial well-order, atomicity, and the theory of strongly rational permutation c
Externí odkaz:
http://arxiv.org/abs/1007.1014