5 papers · 1 filter
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…
A new proof of an EÄecioÄlu--Remmel inverse Kostka matrix problem via a Garsia--Milne involution involving Sym and NSym
Edward E. Allen, Kyle Celano, Sarah K. Mason
EÄecioÄlu and Remmel provide a combinatorial proof (using special rim hook tableaux) that the product of the Kostka matrix and its inverse equals the identity matrix…
Inversions in parking functions
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway +3
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled…
Statistics on -interval parking functions
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway +4
The displacement of a car with respect to a parking function is the number of spots it must drive past its preferred spot in order to park. An -interval parking function is o…
The -positivity of the chromatic symmetric function for twinned paths and cycles
Esther Banaian, Kyle Celano, Megan Chang-Lee +7
The operation of twinning a graph at a vertex was introduced by Foley, Hoà ng, and Merkel (2019), who conjectured that twinning preserves -positivity of the chromatic symmetric…