Raul Felipe Appis,Jaume Llibre
Raul Felipe Appis
Consider the family of polynomial differential systems of degree 3, or simply cubic systems x ' = y , y ' = - x + a 1 x 2 + a 2 x y + a 3 y 2 + a 4 x 3 + a 5 x 2 y + a 6 x y 2 + a 7 y 3 , in the plane R 2 . An equilibrium point ( x 0 ,...
Riccardo W Maffucci
Riccardo W Maffucci
We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary. Ke...
On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks [0.03%]
三维广义投票序列和大串联随机游走的临界指数研究
Michael Wallner
Michael Wallner
We answer some questions on the asymptotics of ballot walks raised in [S. B. Ekhad and D. Zeilberger, April 2021] and prove that these models are not D-finite. This short note demonstrates how the powerful tools developed in the last decade...
Thomas Vetterlein
Thomas Vetterlein
An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the ...
Angular measures and Birkhoff orthogonality in Minkowski planes [0.03%]
Minkowski平面上的角测度和Birkhoff正交性
Márton Naszódi,Vilmos Prokaj,Konrad Swanepoel
Márton Naszódi
Let x and y be two unit vectors in a normed plane R 2 . We say that x is Birkhoff orthogonal to y if the line through x in the direction y supports the unit disc. A B-measure (Fankhänel in Beitr Algebra Geom 52(2):335-342, 2011) is an an...
Benjamin Hackl
Benjamin Hackl
In this brief note a straightforward combinatorial proof for an identity directly connecting rooted forests and unordered set partitions is provided. Furthermore, references that put this type of identity in the context of forest volumes an...