Analogues of up-down permutations for colored permutations.
Analysis of straightening formula.
Another interpretation of the number of derangements. (Une autre interprétation du nombre des dérangements.)
Application of Cauchy's equation in combinatorics and genetics.
Applications of the Finite State Automata for Counting Restricted Permutations and Variations
Arithmetic on blocks.
Arranging numbers on circles to reach maximum total variations.
Ascent sequences and upper triangular matrices containing non-negative integers.
Ascents of size less than d in compositions
A composition of a positive integer n is a finite sequence π1π2...πm of positive integers such that π1+...+πm = n. Let d be a fixed number. We say that we have an ascent of size d or more (respectively, less than d) if πi+1 ≥ πi+d (respectively, πi < πi+1 < πi + d). Recently, Brennan and Knopfmacher determined the mean, variance and limiting distribution of the number of ascents of size d or more in the set of compositions of n. In this paper, we find an explicit formula for the multi-variable...
Avoiding 2-letter signed patterns.