Well quasi-order in combinatorics : embeddings and homomorphisms [PDF]
, 2015 The notion of well quasi-order (wqo) from the theory of ordered sets often arises naturally in contexts where one deals with infinite collections of structures which can somehow be compared, and it then represents a useful discriminator between ‘tame ...
Ruskuc, Nik +3 more
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Pattern classes of permutations via bijections between linearly ordered sets [PDF]
, 2008 A pattern class is a set of permutations closed under pattern involvement or, equivalently, defined by certain subsequence avoidance conditions. Any pattern class X which is atomic, i.e.
Ruškuc, Nik +2 more
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Geometric grid classes of permutations [PDF]
, 2012 A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope ±1 arranged in a rectangular pattern governed by a matrix.
Atkinson, M.D. +8 more
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Inflations of geometric grid classes of permutations [PDF]
, 2015 All three authors were partially supported by EPSRC via the grant EP/J006440/1.Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes.
Ruskuc, Nik, Albert, M.D., Vatter, V.
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On permutation classes defined by token passing networks, gridding matrices and pictures : three flavours of involvement [PDF]
, 2007 The study of pattern classes is the study of the involvement order on finite permutations. This order can be traced back to the work of Knuth. In recent years the area has attracted the attention of many combinatoralists and there have been many ...
Waton, Stephen D.
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An inequality for the weights of two families of sets, their unions and intersections [PDF]
, 1978 Ahlswede R, Daykin DE. An inequality for the weights of two families of sets, their unions and intersections. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete.
Ahlswede, Rudolf, Daykin, David E.
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Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances [PDF]
, 2010 Let ΩΩ be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of ΩΩ, then we write U≈V if there exists a finite subset F of ΩΩ such that the subsemigroup generated by U and F equals that generated by V and F.
Morayne, Michal +11 more
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The extremals of Stanley's inequalities for partially ordered sets [PDF]
, 2023 Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly understood with even ...
Ma, Zhao Yu, Shenfeld, Yair
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A superadditivity and submultiplicativity property for cardinalities of sumsets [PDF]
, 2010 For finite sets of integers A1, . . . ,An we study the cardinality of the n-fold sumset A1 + · · · + An compared to those of (n − 1)-fold sumsets A1 + · · · + Ai−1 + Ai+1 + · · · + An.
Matolcsi, Máté +5 more
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Beyond sum-free sets in the natural numbers [PDF]
, 2014 For an interval [1,N]⊆N, sets S⊆[1,N] with the property that |{(x,y)∈S2:x+y∈S}|=0, known as sum-free sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)=|{(x,y)∈S2:x+y∈S}|, and analyze its behaviour ...
Huczynska, Sophie
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