An infinite antichain of permutations.
An interesting new Mahonian permutation statistic.
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.
Basic calculus of signed permutations. II: Finite analogues of Bessel functions. (Calcul basique des permutations signées. II: Analogues finis des fonctions de Bessel.)
Baxter permutations and plane bipolar orientations.
Baxter permutations. (Permutations de Baxter.)
Bijection between bigrassmannian permutations maximal below a permutation and its essential set.
Binary relations on the power set of an -element set.
Binary strings without zigzags.
Card shuffling and a transformation on Sn.
Cardinality of height function’s range in case of maximally many rectangular islands - computed by cuts
We deal with rectangular m×n boards of square cells, using the cut technics of the height function. We investigate combinatorial properties of this function, and in particular we give lower and upper bounds for the number of essentially different cuts. This number turns out to be the cardinality of the height function’s range, in case the height function has maximally many rectangular islands.