7 papers · 1 filter
Exact enumeration of lozenge tilings of a triangular region
Jun Yan
We prove that the number of lozenge tilings of a certain triangular region is given by the formula \[T_n=\prod_{\substack{1\leq a<b\leq 3n+2\\(a,b)\not=(n+1,2n+2)}}…
An ErdÅs--Szekeres type result for words with repeats
Kyle Celano, Abigail Ollson, Niraj Velankar +1
We prove an ErdÅs--Szekeres type result for finite words over with repeated values. Specifically, we define a \emph{repeat} in a word to be an occurrence of a value w…
Lattice paths enumerations weighted by ascent lengths
Jun Yan
Recent work of the author connected several parking function enumeration problems to enumerations of Catalan paths with respect to certain weight functions that are expressed in te…
Multivalued forbidden numbers of two-rowed configurations -- the missing cases
Wallace Peaslee, Attila Sali, Jun Yan
The present paper considers extremal combinatorics questions in the language of matrices. An -matrix is a matrix with entries in . An -matrix is simple i…
Exponential odd-distance sets under the Manhattan metric
Alberto Espuny DÃaz, Emma Hogan, Freddie Illingworth +3
We construct a set of points in such that all pairwise Manhattan distances are odd integers, which improves the recent linear lower bound of Golovanov, Kupavsk…
Results on pattern avoidance in parking functions
Jun Yan
In this paper, we mainly study two notions of pattern avoidance in parking functions. First, for any collection of length 3 patterns, we compute the number of parking functions of…