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1324-Avoiding (0,1)-Matrices
Get PDFA 1324-avoiding (0,1)-matrix is an × matrix that does not contain the 1324-pattern. Our goal is to find the maximum number of 1’s that an × 1324-avoiding (0,1)-matrix can contain. We build upon Brualdi and Cao’s recent work, where they characterized the × 1234-avoiding matrices with the maximum number of 1’s. They found that these matrices can contain up to 3( + − 3) 1’s. We originally conjectured that 1324-avoiding matrices must contain at most the same number of 1’s, as is the case with the six patterns formed by permutations of {1,2,3}. However, we have found 1324-avoiding matrices that contain more 1’s than those that are 1234-avoiding, and we provide a conjecture for the maximum number of 1’s that a 1324-avoiding matrix can contain
Generating trees of (reducible) 1324-avoiding permutations
No full textWe consider permutations that avoid the pattern 1324. We give exact formulas for the number of reducible 1324-avoiding permutations and the number of {1324, 4132, 2413, 3241}avoiding permutations. By studying the generating tree for all 1324-avoiding permutations, we obtain a recurrence formula for their number. A computer program provides data for the number of 1324-avoiding permutations of length up to 20
Generating Trees of (Reducible) 1324-avoiding Permutations
No full textWe consider permutations that avoid the pattern 1324. We give exact formulas for thenumber of reducible 1324-avoiding permutations and the number of {1324, 4132, 2413, 3241}-avoiding permutations. By studying the generating tree for all 1324-avoiding permutations,we obtain a recurrence formula for their number. A computer program provides data for thenumber of 1324-avoiding permutations of length up to 20
A positional statistic for 1324-avoiding permutations
Get PDFWe consider the class of permutations of size that avoid the pattern 1324 and examine the subset of elements for which , . This notation means that, when written in one line notation, such a permutation must have to the left of , and the elements of must all be to the right of . For , we establish a connection between the subset of permutations in having the 1 adjacent to the (called primitives), and the set of 1324-avoiding dominoes with points. For , we introduce constructive algorithms and give formulas for the enumeration of by the position of relative to the position of . For , we formulate some conjectures for the corresponding generating functions.10 pages. Final versio
Enumerating 1324-avoiders with few inversions
Get PDFWe enumerate the numbers of 1324-avoiding -permutations with exactly inversions for all and . The result depends on a structural characterization of such permutations in terms of a new notion of almost-decomposability. In particular, our enumeration verifies half of a conjecture of Claesson, Jelínek and Steingrímsson, according to which for all and . Proving also the other half would improve the best known upper bound for the exponential growth rate of the number of -avoiders from to approximately .23 page
Counting 1324-avoiding Permutations
No full textWe consider permutations that avoid the pattern 1324. By studying the generating tree for such permutations, we obtain a recurrence formula for their number. A computer program provides data for the number of 1324-avoiding permutations of length up to 20.
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Inscriptions 1324 à 1329
No full textInscriptions 1324 à 1329. In: Revue épigraphique, tome 4, N°96, 1900. pp. 79-86
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