15 citations · 57 across the 12 of their papers we have counts for
12 papers · 1 filter
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…
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…
Independent sets in certain classes of (almost) regular graphs
Alexander Burstein, Sergey Kitaev, Toufik Mansour
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between the…
The problem of the pawns
S. Kitaev, T. Mansour
In this paper we study the number of ways to place nonattacking pawns on an chessboard. We find an upper bound for and analyse its asymptotic behavi…
The Peano curve and counting occurrences of some patterns
S. Kitaev, T. Mansour
We introduce Peano words, which are words corresponding to finite approximations of the Peano space filling curve. We then find the number of occurrences of certain patterns in the…