Abstract.
We consider the number of permutations with prescribed up-down structure as a function of two arguments: the number n of elements and the introduced up-down index k of a permutation. We consider sets of permutations for which k is a fixed number and when k is a function of n. In the first case the number of permutations is a polynomial in n, the degree of which is defined by k.
Received: 2010-09-27
Revised: 2011-06-30
Accepted: 2011-11-20
Published Online: 2012-08-01
Published in Print: 2012-08-01
© 2012 by Walter de Gruyter Berlin Boston
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Artikel in diesem Heft
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- On Weakly Complete Sequences Formed by the Greedy Algorithm
- Bijective Proofs of Vajda's Ninetieth Fibonacci Number Identity and Related Identities
- Newman Polynomials, Reducibility, and Roots on the Unit Circle
- A Property of Twin Primes
- Number of Permutations with Prescribed Up-Down Structure as a Function of Two Variables
- A -Expansion Associated to Sturmian Sequences
- On the Number of Carries Occurring in an Addition Mod
- A Probabilistic Look at Series Involving Euler's Totient Function
- Fibonacci Variations of a Conjecture of Polignac
- Extending Nathanson Heights to Arbitrary Finite Fields
- On the Maximal Cross Number of Unique Factorization Zero-Sum Sequences over a Finite Abelian Group
- An Explicit Bound for Aliquot Cycles of Repdigits
- A Note on the Minimal Number of Representations in
- A Unified Proof of Two Classical Theorems on CNS Polynomials
- On the Problem of Molluzzo for the Modulus 4
- On Multiplicative Functions with Bounded Partial Sums
- Avoiding Type or Patterns in a Partition of a Set
Schlagwörter für diesen Artikel
Alternating Permutations;
Eulerian Numbers;
Niven's Signature for Permutations
Artikel in diesem Heft
- Masthead
- On Weakly Complete Sequences Formed by the Greedy Algorithm
- Bijective Proofs of Vajda's Ninetieth Fibonacci Number Identity and Related Identities
- Newman Polynomials, Reducibility, and Roots on the Unit Circle
- A Property of Twin Primes
- Number of Permutations with Prescribed Up-Down Structure as a Function of Two Variables
- A -Expansion Associated to Sturmian Sequences
- On the Number of Carries Occurring in an Addition Mod
- A Probabilistic Look at Series Involving Euler's Totient Function
- Fibonacci Variations of a Conjecture of Polignac
- Extending Nathanson Heights to Arbitrary Finite Fields
- On the Maximal Cross Number of Unique Factorization Zero-Sum Sequences over a Finite Abelian Group
- An Explicit Bound for Aliquot Cycles of Repdigits
- A Note on the Minimal Number of Representations in
- A Unified Proof of Two Classical Theorems on CNS Polynomials
- On the Problem of Molluzzo for the Modulus 4
- On Multiplicative Functions with Bounded Partial Sums
- Avoiding Type or Patterns in a Partition of a Set