The ith cycle minor of a permutation p of the set {1, 2, . . . , n} is the permutation formed by deleting an entry i from the decomposition of p into disjoint cycles and reducing each remaining entry larger than i by 1. In this paper, we show that any permutation of {1, 2, . . . , n} can be reconstructed from its set of cycle minors if and only if n ≥ 6. We then use this to provide an alternate...

With every linear code is associated a permutation group whose cycle index is the weight enumerator of the code (up to a trivial normalisation). There is a class of permutation groups (the IBIS groups) which includes the groups obtained from codes as above. With every IBIS group is associated a matroid; in the case of a group from a code, the matroid differs only trivially from that which arise...

We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n! Hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices P, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. A graph instance (G) is initially coded as exclusion set ...

With every linear code is associated a permutation group whose cycle index is the weight enumerator of the code (up to normalisation). There is a class of permutation groups (the IBIS groups) which includes the groups obtained from codes as above. With every IBIS group is associated a matroid; in the case of a code group, the matroid differs only trivially from that which arises from the code. ...

We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that use...

Let Fq be a finite field with q elements and suppose C is a conjugation class of permutations of the elements of Fq . We denote by C = (c1; c2; . . . ; ct ) the conjugation class of permutations that admit a cycle decomposition with ci i-cycles (i = 1, . . . , t). Further, we set c = 2c2+· · ·+ tct = q−c1 to be the number of elements of Fq moved by any permutation in C. If ∈ C, then the permuta...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...

A number of fields, including genome rearrangements and interconnection network design, are concerned with sorting permutations in “as few moves as possible”, using a given set of allowed operations. These often act on just one or two segments of the permutation, e.g. by reversing one segment or exchanging two segments. The cycle graph of the permutation to sort is a fundamental tool in the the...

In this paper, we propose a 1-cycle high-performance 3D bufferless router with a 3-stage permutation network. The proposed router utilizes the 3-stage permutation network instead of the serialized switch allocator and 7× 7 crossbar to achieve the frequency of 1.25GHz in TSMC 65nm technology. Compared with the other two 3D bufferless routers, the proposed router occupies less area and consumes l...

Python implementation of permutations is presented. Three classes are introduced: Perm for permutations, Group for permutation groups, and PermError to report any errors for both classes. The class Perm is based on Python dictionaries and utilize cycle notation. The methods of calculation for the perm order, parity, ranking and unranking are given. A random permutation generation is also shown....