88,246 research outputs found
Many Different Uniformity Numbers of Yorioka Ideals
Using a countable support product of creature forcing posets, we show that
consistently, for uncountably many different functions the associated Yorioka
ideals' uniformity numbers can be pairwise different. In addition we show that,
in the same forcing extension, for two other types of simple cardinal
characteristics parametrised by reals (localisation and anti-localisation
cardinals), for uncountably many parameters the corresponding cardinals are
pairwise different.Comment: 29 pages, 4 figure
On conjugacy growth of linear groups
We investigate the conjugacy growth of finitely generated linear groups. We
show that finitely generated non-virtually-solvable subgroups of GL_d have
uniform exponential conjugacy growth and in fact that the number of distinct
polynomials arising as characteristic polynomials of the elements of the ball
of radius n for the word metric has exponential growth rate bounded away from 0
in terms of the dimension d only.Comment: 21 page
Promotion and Rowmotion
We present an equivariant bijection between two actions--promotion and
rowmotion--on order ideals in certain posets. This bijection simultaneously
generalizes a result of R. Stanley concerning promotion on the linear
extensions of two disjoint chains and recent work of D. Armstrong, C. Stump,
and H. Thomas on root posets and noncrossing partitions. We apply this
bijection to several classes of posets, obtaining equivariant bijections to
various known objects under rotation. We extend the same idea to give an
equivariant bijection between alternating sign matrices under rowmotion and
under B. Wieland's gyration. Finally, we define two actions with related orders
on alternating sign matrices and totally symmetric self-complementary plane
partitions.Comment: 25 pages, 22 figures; final versio
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