Related papers: The cycle enumerator of unimodal permutations

Considering commutator monomials of the non-commutative associative variables $X_1,\ldots,X_n$; we determine the maximal possible number of alternating associative monomials in their noncommutative polynomial expansions. This is achieved by…

In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences,…

The simplicial endofunctor induced by a comonad in some category may underly a cyclic object in its category of endofunctors. The cyclic symmetry is then given by a sequence of natural transformations. We write down the commutation…

We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…

A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal binomial coefficients are derived, new identities are obtained,…

Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…

In this paper we provide a unified combinatorial approach to establish a connection between Stirling permutations, cycle structures of permutations and perfect matchings. The main tool of our investigations is MY-sequences. In particular,…

Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G.

This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…

Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…

We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in formulas for characters of certain representations of the symmetric group. Such formulas…

We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

A mutation cycle is a cycle in a graph whose vertices are labeled by the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed $n\ge 4$, we describe arbitrarily long mutation cycles involving…

We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive…

We translate Uchimura's identity for the divisor function and whose generalizations into combinatorics of partitions, and give a combinatorial proof of them. As a by-product of their proofs, we obtain some combinatorial results.

We determine the permutation groups that arise as the automorphism groups of cyclic combinatorial objects. As special cases we classify the automorphism groups of cyclic codes. We also give the permutations by which two cyclic combinatorial…

As well known, permanent of a square (0,1)-matrix $A$ of order $n$ enumerates the permutations $\beta$ of $1,2,...,n$ with the incidence matrices $B\leq A.$ To obtain enumerative information on even and odd permutations with condition…

In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…

The simple permutations in two permutation classes --- the 321-avoiding permutations and the skew-merged permutations --- are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards…