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464  Articles
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In this paper we study the cycle descent statistic on permutations. Several involutions on permutations and derangements are constructed. Moreover, we construct a bijection between negative cycle descent permutations and Callan perfect matchings.

Let GG be a graph whose vertices are labeled 1,…,n1,\ldots,n, and p\pi be a permutation on [n]:={1,2,…,n}[n]:=\{1,2,\ldots, n\}. A pebble pip_i that is initially placed at the vertex ii has destination p(i)\pi(i) for each i?[n]i\in [n]. At each step, we c... see more

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

In this paper, we study the relationship among left peaks, interior peaks and up-down runs of simsun permutations. Properties of the generating polynomials, including the recurrence relation, generating function and real-rootedness are studied. Moreover, ... see more

The decoding of Kogoj’s intriguing numerical labelling of chords in this discussion presents an important step ahead in understanding of Kogoj’s invention of so-called chord permutations. The use of those is confirmed and situated within an aesthetic and ... see more

The decoding of Kogoj’s intriguing numerical labelling of chords in this discussion presents an important step ahead in understanding of Kogoj’s invention of so-called chord permutations. The use of those is confirmed and situated within an aesthetic and ... see more

This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction recovers the class... see more

This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction recovers the class... see more

Let G be a permutation group on a set with no fixed points in and let m be a positive integer.If no element of G moves any subset of by more than m points (that is, if |

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