Eulerian Central Limit Theorems and Carlitz identities in positive elements of Classical Weyl Groups

2020/05/26 by Dey, Hiranya Kishore, Sivasubramanian, Sivaramakrishnan
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.12631

Abstract

Central Limit Theorems are known for the Eulerian statistic "descent" (or "excedance") in the symmetric group \SSS_n. Recently, Fulman, Kim, Lee and Petersen gave a Central Limit Theorem for "descent" over the alternating group \AAA_n and also gave a Carlitz identity in \AAA_n using descents. In this paper, we give a Central Limit Theorem in \AAA_n involving excedances. We extend these to the positive elements in type B and type D Coxeter groups. Boroweic and Młotkowski enumerated type B descents over \DD_n, the type D Coxeter group and gave similar results. We refine their results for both the positive and negative part of \DD_n. Our results are a consequence of signed enumeration over these subsets.

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