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Avelines's Hole: An Unexpected Twist in the Tale
(University of Bristol Spelaeological Society, 2019)
Aveline’s Hole is the largest known Early Mesolithic cemetery in Britain, previously thought to have no evidence for subsequent burial activity. Thus, it came as some surprise when the results of a recent ancient human DNA ...
Growth rate of binary words avoiding xxxR
(Elsevier, 2016-01)
Abstract
Consider the set of those binary words with no non-empty factors of the form
xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows
polynomially or exponentially with length. In this ...
Infinite words containing squares at every position
(EDP Sciences, 2010)
Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve ...
Multi-dimensional sets recognizable in all abstract numeration systems
(EDP Sciences, 2011)
We prove that the subsets of Nd that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.
Skeleton Cave, Leigh Woods, Bristol
(University of Bristol Spelaeological Society, 2017)
An account is given of the discovery and excavation of this small cave in the 1960s. It is recorded that archaeological finds were made, but of these, only a single human mandible can now be traced. Radiocarbon dating shows ...
The minimal automaton recognizing mN in a linear numeration system
(Integers, 2011-12-02)
We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component ...
Further applications of a power series method for pattern avoidance
(The Electronic Journal of Combinatorics, 2011-06-21)
In combinatorics on words, a word w over an alphabet ∑ is said to avoid a pattern
p over an alphabet ∆ if there is no factor x of w and no non-erasing morphism h
from ∆* to ∑* such that h(p) = x. Bell and Goh have recently ...
Avoiding three consecutive blocks of the same size and same sum
(Association of Computing Machinery, 2014-04)
We show that there exists an infinite word over the alphabet {0,1,3,4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from1994.
Cyclic Complexity of Some Infinite Words and Generalizations
(Integers, 2018-03)
Cassaigne et al. introduced the cyclic complexity function c_x(n), which gives the number of cyclic conjugacy classes of length-n factors of a word x. We study the behavior of this function for the Fibonacci word f and the ...
Generating self-complementary uniform hypergraphs
(Discrete Mathematics, 2010-02)
In 2007, Szymanski and Wojda proved that for positive integers n; k with k less than n, a self-complementary k-uniform hypergraph of order n exists if and only if n/k is even. In this paper, we characterize the cycle type ...