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Classifying Descents According to Parity
Sergey Kitaev, Jeffrey Remmel
In this paper we refine the well-known permutation statistic "descent" by fixing parity of (exactly) one of the descent's numbers. We provide explicit formulas for the distribution…
Enumerating Segmented Patterns in Compositions and Encoding by Restricted Permutations
Sergey Kitaev, Tyrrell B. McAllister, T. Kyle Petersen
A composition of a nonnegative integer (n) is a sequence of positive integers whose sum is (n). A composition is palindromic if it is unchanged when its terms are read in reverse o…
The number of matroids on a finite set
W. M. B. Dukes
In this paper we highlight some enumerative results concerning matroids of low rank and prove the tail-ends of various sequences involving the number of matroids on a finite set to…
On unavoidable sets of word patterns
Alexander Burstein, Sergey Kitaev
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets o…