Combinatorics of permutations

• Provide a bijection combinatorial proof for the facts that The number of derangements of length n equals the number of permutations of length n that have ...

A derangement is a permutation in which no entry is at its original position. The number of derangements of [ n ] is called the “derangement number” or “de Montmort number”, and is denoted by D n. The sequence { D n } enumerates, in ...

A family of permutations A@__ __S"n is said to be t-intersecting if any two permutations in A agree on at least t points, i.e. for any @s,@p@__ __A, |{i@__ __[n]:@s(i)=@p(i)}|>=t. It was proved by Friedgut, Pilpel and the author in [6] that for n ...

A permutation is called parity alternating if its entries assume even and odd integers alternately. Parity alternating permutations form a subgroup of the symmetric group. This paper deals with the number of permutations classified by the ascent number. ...