A pattern avoidance criterion for free inversion arrangements
نویسندگان
چکیده
منابع مشابه
Left-right arrangements, set partitions, and pattern avoidance
We show structural properties of the system of ordered partitions of [n] := {1, . . . , n} all of whose left-to-right minima occur in odd locations, called left-to-right arrangements. Our main objectives are (i) to show that the set of all finite left-to-right arrangements is a projective system under a natural choice of restriction operation, (ii) to establish a non-trivial embedding of set pa...
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Let W be a finite Coxeter group. For a given w ∈ W , the following assertion may or may not be satisfied: (∗) The principal Bruhat order ideal of w contains as many elements as there are regions in the inversion hyperplane arrangement of w. We present a type independent combinatorial criterion which characterises the elements w ∈ W that satisfy (∗). A couple of immediate consequences are derive...
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The many-to-one mapping from representations in the speech articulatory space to acoustic space renders the associated acoustic-to-articulatory inverse mapping non-unique. Among various techniques, imposing smoothness constraints on the articulator trajectories is one of the common approaches to handle the non-uniqueness in the acoustic-to-articulatory inversion problem. This is because, articu...
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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, and the many open problems that still remain. Section 1 of this paper provides definitions, notations, and some properties o...
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Cassaigne conjectured in 1994 that any pattern with m distinct variables of length at least 3(2m−1) is avoidable over a binary alphabet, and any pattern with m distinct variables of length at least 2 is avoidable over a ternary alphabet. Building upon the work of Rampersad and the power series techniques of Bell and Goh, we obtain both of these suggested strict bounds. Similar bounds are also o...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2016
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-015-0663-5