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We establish a lower bound of 10.271 for the growth rate of the permutations avoiding 1324, and an upper bound of 13.5. ... This is done by first finding the precise growth rate of a subclass whose enumeration is related to West-2-stack-sortable permutations, and then combining copies of this subclass in particular ways. ... on the growth rate of Av(1324). ...doi:10.1016/j.endm.2017.06.029 fatcat:cpm6ikzb2vhk3mjy34fr4pprrm
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permutations avoiding the pattern 1324, and an improved upper bound of 13.5. ... These results depend on a new exact structural characterisation of 1324-avoiders as a subclass of an infinite staircase grid class, together with precise asymptotics of a small domino subclass whose enumeration ... We are grateful to Vince Vatter, who was asked by the first two authors to present this conjecture in the problem session at the Permutation Patterns 2016 conference, which they were unable to attend. ...arXiv:1711.10325v3 fatcat:dsyoz34ujve7vebwfbvhtn6p5i
We then apply Combinatorial Exploration to the domain of permutation patterns, to great effect. We rederive hundreds of results in the literature in a uniform manner and prove many new ones. ... These results can be found in a new public database, the Permutation Pattern Avoidance Library (PermPAL) at https://permpal.com. ... Acknowledgments We would like to thank the many undergraduate and masters students with whom we had invaluable discussions and who contributed to this work, including (with references to their theses when ...arXiv:2202.07715v1 fatcat:3iutygbjcnc4jbe4kkuvbsyo5m
This study examines the epigraphic evidence and literary texts relating to the slaves, freed slaves, and staff of the households of the Julio-Claudians. ... The epigraphic evidence plainly illustrates the shift from senatorial household to Imperial household, the development of separate domestic and civil service components, and the gradual formation of a ... Sulpicius Faustus by the next Kalends of November, by Jupiter Optimus Maximus and by the spirit of the divine Augustus and by the genius of C. ...doi:10.11575/prism/28131 fatcat:ucuru3ke6rd5fbqn7us3thigcq
Unusually this 0.45m diameter tree exhibited the slow even growth rate (1.5-1.0mm) of pre twelfth-century timber, rather than the more vigorous grow rate of most contemporary timbers, it was also old as ... There were also two dominoes, the 5-4 and 2-2 spots ( Fig. 5 .43I-J). ... This is an important book, and the scale of the investigations and the richness of the archaeology make it a major contribution to studies of British town suburbs and boundaries in particular and urban ...doi:10.17863/cam.55571 fatcat:xza5qf7nizcv3btd4u4dkdubce
of the individual and comm [...] ... By uniting the concerns of codicology and cultural history, we can gain new insights into the effect of each manuscript's textual sequences while also considering the effect of the distribution of texts ... rate. ...doi:10.20381/ruor-4035 fatcat:jpkuzchjqvhpzfirbzqpdhe2y4