Related papers: Mutation Cycles from Reddening Sequences

In symmetric groups, studies of permutation factorizations or triples of permutations satisfying certain conditions have a long history. One particular interesting case is when two of the involved permutations are long cycles, for which…

The cyclic sieving phenomenon provides a link between a polynomial analogue of Gauss congruence known as $q$-Gauss congruence, and a combinatorial analogue of Gauss congruence based on sequences of cyclic group actions. We strengthen this…

We give a combinatorial mutation rule for Aihara's and Iyama's silting mutation. As an application, we reprove Keller-Yang's mutation rule for Ginzburg algebras, and obtain an analog of that rule for arbitrary dimension.

We show a method in constructing algebraic cycles via intersection theory. It leads to a proof of the Lefschetz standard conjecture.

We give a generating function for the number of unimodal permutations with a given cycle structure.

Sidon sequences and their generalizations have found during the years and especially recently various applications in coding theory. One of the most important applications of these sequences is in the connection of synchronization patterns.…

We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by the exchange matrix. The simplest example is the Lyness…

Motivated by cryptographic applications, we investigate two machine learning approaches to modular multiplication: namely circular regression and a sequence-to-sequence transformer model. The limited success of both methods demonstrated in…

We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.

For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…

We consider the cycle structure of a random permutation $\sigma$ chosen uniformly from the symmetric group, subject to the constraint that $\sigma$ does not contain cycles of length exceeding $r.$ We prove that under suitable conditions the…

We give a proof of the cyclicity conjecture of Akasaka-Kashiwara, for simply laced types, via quiver varieties. We get also an algebraic characterization of the standard modules.

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…

Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially $q$-analogues, have useful interpretations related to actions and representations of the cyclic group. We propose a definition of sieving for an…

In this paper, we count a dual set of Stirling permutations by the number of alternating runs. Properties of the generating functions, including recurrence relations, grammatical interpretations and convolution formulas are studied.

In general, the existence of a maximal green sequence is not mutation invariant. In this paper we show that it is in fact mutation invariant for cluster quivers of finite mutation type. In particular, we show that a mutation finite cluster…

We describe several families of permutation polynomials obtained using functions with linear translators.

We use a geometric description of $m$-cluster categories of Dynkin type $A$ to count the the number of coloured quivers in the $m$-mutation class of quivers of Dynkin type $A$. This is related to angulations of polygons and the cell-growth…

Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…

We consider a class of non-local reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. For a confining fitness function, we prove well-posedness and write the solution explicitly, via some…