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pro vyhledávání: '"Conway, Andrew R. A."'
Autor:
Conway, Andrew R, Guttmann, Anthony J
We develop a new, powerful method for counting elements in a multiset. As a first application, we use this algorithm to study the number of occurrences of patterns in a permutation. For patterns of length 3 there are two Wilf classes, and the general
Externí odkaz:
http://arxiv.org/abs/2306.12682
Building a theoretical understanding of the capabilities of large language models (LLMs) is vital for our ability to predict and explain the behavior of these systems. Here, we investigate the structure of LLM capabilities by extracting latent capabi
Externí odkaz:
http://arxiv.org/abs/2306.10062
Pattern-avoiding ascent sequences have recently been related to set-partition problems and stack-sorting problems. While the generating functions for several length-3 pattern-avoiding ascent sequences are known, those avoiding 000, 100, 110, 120 are
Externí odkaz:
http://arxiv.org/abs/2111.01279
We have made a systematic numerical study of the 16 Wilf classes of length-5 classical pattern-avoiding permutations from their generating function coefficients. We have extended the number of known coefficients in fourteen of the sixteen classes. Ca
Externí odkaz:
http://arxiv.org/abs/2109.13485
Akademický článek
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We give an improved algorithm for counting the number of $1324$-avoiding permutations, resulting in $14$ further terms of the generating function, which is now known for all patterns of length $\le 50$. We re-analyse the generating function and find
Externí odkaz:
http://arxiv.org/abs/1709.01248
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol. 19 no. 2, Permutation Patterns 2016, Permutation Patterns (February 26, 2018) dmtcs:3311
We review and extend what is known about the generating functions for consecutive pattern-avoiding permutations of length 4, 5 and beyond, and their asymptotic behaviour. There are respectively, seven length-4 and twenty-five length-5 consecutive-Wil
Externí odkaz:
http://arxiv.org/abs/1704.08839
Akademický článek
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Autor:
Moore, Dawn Michele1 (AUTHOR) dawn.moore@cgu.edu, Conway, Andrew R. A.2 (AUTHOR)
Publikováno v:
Journal of Intelligence. May2023, Vol. 11 Issue 5, p90. 22p.
Autor:
Conway, Andrew R.
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper covers the de
Externí odkaz:
http://arxiv.org/abs/1610.09806