2,717 research outputs found
Number of pop-stacked permutations
No full textThe number of pop-stacked permutations of [n] for n = 1 to 1000 (sequence A307030 in the OEIS) as well as a triangle of numbers giving the number of pop-stacked permutations of each length grouped by number of ascending runs up to n = 300
Guenther Anders.
No full textDigital ImageThe author Guenther Anders was born on July 12, 1902 in Breslau, the son of William Stern.4607
Enumerating permutations avoiding a pair of Babson-Steingrimsson patterns
No full textBabson and Steingrimsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Subsequently, Claesson presented a complete solution for the number of permutations avoiding any single pattern of type (1, 2) or (2, 1). For eight of these twelve patterns the answer is given by the Bell numbers. For the remaining four the answer is given by the Catalan numbers. In the present paper we give a complete solution for the number of permutations avoiding a pair of patterns of type (1, 2) or (2, 1). We also conjecture the number of permutations avoiding the patterns in any set of three or more such patterns
Enumerating permutations avoiding a pair of BabsonSteingrímsson patterns
No full textAbstract. Babson and Steingrímsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Subsequently, Claesson presented a complete solution for the number of permutations avoiding any single pattern of type (1, 2) or (2, 1). For eight of these twelve patterns the answer is given by the Bell numbers. For the remaining four the answer is given by the Catalan numbers. In the present paper we give a complete solution for the number of permutations avoiding a pair of patterns of type (1, 2) or (2, 1). We also conjecture the number of permutations avoiding the patterns in any set of three or more such patterns. 1
Anders Bodelsen
No full textThis is a short presentation of the main works of the Danish author Anders Bodelsen
Enumerating permutations avoiding a pair of Babson-Steingrimsson patterns
No full textBabson and Steingrimsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Subsequently, Claesson presented a complete solution for the number of permutations avoiding any single pattern of type (1, 2) or (2, 1). For eight of these twelve patterns the answer is given by the Bell numbers. For the remaining four the answer is given by the Catalan numbers. In the present paper we give a complete solution for the number of permutations avoiding a pair of patterns of type (1, 2) or (2, 1). We also conjecture the number of permutations avoiding the patterns in any set of three or more such patterns
matchings, posets (extended abstract)
No full textWe show that there are matchings on points without, so called, left (neighbor) nestings. We also define a set of naturally labelled -free posets, and show that there are such posets on elements. Our work was inspired by Bousquet-Mélou, Claesson, Dukes and Kitaev [J. Combin. Theory Ser. A. 117 (2010) 884―909]. They gave bijections between four classes of combinatorial objects: matchings with no neighbor nestings (due to Stoimenow), unlabelled -free posets, permutations avoiding a specific pattern, and so called ascent sequences. We believe that certain statistics on our matchings and posets could generalize the work of Bousquet-Mélou et al. and we make a conjecture to that effect. We also identify natural subsets of matchings and posets that are equinumerous to the class of unlabeled -free posets. We give bijections that show the equivalence of (neighbor) restrictions on nesting arcs with (neighbor) restrictions on crossing arcs. These bijections are thought to be of independent interest. One of the bijections maps via certain upper-triangular integer matrices that have recently been studied by Dukes and Parviainen [Electron. J. Combin. 17 (2010) #R53].Nous montrons qu'il y a couplages sur points sans emboîtement (de voisins) à gauche. Nous définissons aussi un ensemble d'EPO (ensembles partiellement ordonnés) sans motif naturellement étiquetés, et montrons qu'il y a tels EPO sur éléments. Notre travail a été inspiré par Bousquet-Mélou, Claesson, Dukes et Kitaev [J. Combin. Theory Ser. A. 117 (2010) 884―909]. Ces auteurs donnent des bijections entre quatre classes d'objets combinatoires: couplages sans emboîtement de voisins (dû à Stoimenow), EPO sans motif non étiquetés, permutations évitant un certain motif, et des objets appelés suites à montées. Nous pensons que certaines statistiques sur nos couplages et nos EPO pourraient généraliser le travail de Bousquet-Mélou et al. et nous proposons une conjecture à ce sujet. Nous identifions aussi des sous-ensembles naturels de couplages et d'EPO qui sont énumérés par la même séquence que la classe des EPO sans motif non étiquetés. Nous donnons des bijections qui démontrent l'équivalence entre les restrictions sur les emboîtements (d'arcs voisins) et les restrictions sur les croisements (d'arcs voisins). Nous pensons que ces bijections présentent un intérêt propre. L'une de ces bijections passe par certaines matrices triangulaires supérieures à coefficients entiers qui ont été récemment étudiées par Dukes et Parviainen [Electron. J. Combin. 17 (2010) #R53]
Pattern avoidance in partial permutations
No full textMotivated by the concept of partial words, we introduce an analogous concept of partial permutations. A partial permutation of length n with k holes is a sequence of symbols in which each of the symbols from the set {1,2,...,n-k} appears exactly once, while the remaining k symbols of are "holes". We introduce pattern-avoidance in partial permutations and prove that most of the previous results on Wilf equivalence of permutation patterns can be extended to partial permutations with an arbitrary number of holes. We also show that Baxter permutations of a given length k correspond to a Wilf-type equivalence class with respect to partial permutations with (k-2) holes. Lastly, we enumerate the partial permutations of length n with k holes avoiding a given pattern of length at most four, for each n >= k >= 1
Binnenstedelijk ontwikkelen moet op alle fronten anders
No full textBinnenstedelijke (her)ontwikkeling moet vraaggerichter, goedkoper, flexibeler en sneller, anders loopt de stedelijke vernieuwing compleet vast. Ook ambities vergen aanpassing. Dit artikel laat de urgentie van dit probleem zien, maar schetst vooral hoe het anders moet en kan, met een focus op actuele discussiepuntenReal Estate and HousingArchitectur
n! matchings, n! posets
No full textWe show that there are matchings on points without, so called, left (neighbor) nestings. We also define a set of naturally labeled -free posets, and show that there are such posets on elements. Our work was inspired by Bousquet-M\'elou, Claesson, Dukes and Kitaev [J. Combin. Theory Ser. A. 117 (2010) 884--909]. They gave bijections between four classes of combinatorial objects: matchings with no neighbor nestings (due to Stoimenow), unlabeled -free posets, permutations avoiding a specific pattern, and so called ascent sequences. We believe that certain statistics on our matchings and posets could generalize the work of Bousquet-M\'elou et al.\ and we make a conjecture to that effect. We also identify natural subsets of matchings and posets that are equinumerous to the class of unlabeled -free posets. We give bijections that show the equivalence of (neighbor) restrictions on nesting arcs with (neighbor) restrictions on crossing arcs. These bijections are thought to be of independent interest. One of the bijections maps via certain upper-triangular integer matrices that have recently been studied by Dukes and Parviainen [Electron. J. Combin. 17 (2010) \#R53
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