Related papers: Generating permutations with a given major index
We introduce a new framework for solving an important class of computational problems involving finite permutation groups, which includes calculating set stabilisers, intersections of subgroups, and isomorphisms of combinatorial structures.…
We give a bijection between meanders and special sorts of Gauss diagrams which aroused from the Thurston generators of braid groups. It allows us to give an algorithm to construct such diagrams and to code meanders by matrices which are…
We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…
We study an interesting family of cooperating coroutines, which is able to generate all patterns of bits that satisfy certain fairly general ordering constraints, changing only one bit at a time. (More precisely, the directed graph of…
Counterfactual explanations promote explainability in machine learning models by answering the question "how should an input instance be perturbed to obtain a desired predicted label?". The comparison of this instance before and after…
We introduce a class of rooted graphs which allows one to encode various kinds of classical or quantum circuits. We then follow a set-theoretic approach to define rewrite systems over the considered graphs and propose a new complete…
An algorithm is presented for unranking permutations in transposition order: Given a seed s\in N, the algorithm produces a permutation P(s) that differs from the permutation P(s+1) by the transposition of two elements.
We introduce a new method for encoding permutations as weighted independent sets in a family of graphs we call cores. The encoding allows us to enumerate (1324, 2143)-, (1234, 1324, 2143)-, (1234, 1324, 1432, 3214)-avoiding permutations…
Multiple sequence alignment is a key process in today's biology, and finding a relevant alignment of several sequences is much more challenging than just optimizing some improbable evaluation functions. Our approach for addressing multiple…
A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes.…
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…
We introduce alphabet-permutation (AP) codes, a new family of error-correcting codes defined by iteratively applying random coordinate-wise permutations to a fixed initial word. A special case recovers random additive codes and random…
We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…
In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we…
An $n$-bit Gray code is a sequence of all $n$-bit strings such that consecutive strings differ in a single bit. It is well-known that given $\alpha,\beta\in\{0,1\}^n$, an $n$-bit Gray code between $\alpha$ and $\beta$ exists iff the Hamming…
Sparse superposition codes were originally proposed as a capacity-achieving communication scheme over the gaussian channel, whose coding matrices were made of i.i.d. gaussian entries.We extend this coding scheme to more generic ensembles of…
In this paper, we consider coding of short data frames (192 bits) by IRA codes. A new interleaver for the IRA codes based on a Gruenbaum graph is proposed. The difference of the proposed algorithm from known methods consists in the…
In this paper, we consider the problem of generating a set of counterfactual explanations for a group of instances, with the one-for-many allocation rule, where one explanation is allocated to a subgroup of the instances. For the first…
Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking. In this paper we formalize these procedures and develop…
We prove the conjecture by M. Yip stating that counting genus one partitions by the number of their elements and parts yields, up to a shift of indices, the same array of numbers as counting genus one rooted hypermonopoles. Our proof…