Related papers: Fix-Mahonian Calculus, I: two transformations

We derive a system of fixed-point equations for the equilibrium transfers in a class of one-to-one matching models with linear transferable utility. We then show that, when the degree of substitution between alternatives is bounded from…

Permutation statistics constitute a classical subject of enumerative combinatorics. In her study of the genus zeta function, Denert discovered a new Mahonian statistic for permutations, which is called the Denert's statistic ({\bf $\den$})…

We prove two general decomposition theorems for fixed-point invariants: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar additivity results for these invariants. Moreover, the proofs of…

Planar central configurations can be seen as critical points of the reduced potential or solutions of a system of equations. By the homogeneity and invariance of the potential with respect to SO(2), it is possible to see that the…

We obtain a general lower bound for the number of fixed points of a circle action on a compact almost complex manifold $M$ of dimension $2n$ with nonempty fixed point set, provided the Chern number $c_1c_{n-1}[M]$ vanishes. The proof…

In the framework of the renormalization-group theory of critical phenomena, a quantitative description of many continuous phase transitions can be obtained by considering an effective $\Phi^4$ theories, having an N-component fundamental…

Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe…

In this paper, we shall show that some coincidence point and common fixed point results for three or four mappings could easily be obtained from the corresponding fixed point results for two mappings.

We consider 2-local geometries and other subgroup complexes for sporadic simple groups. For six groups, the fixed point set of a noncentral involution is shown to be equivariantly homotopy equivalent to a standard geometry for the component…

Let $X=(V,E)$ be a finite simple connected graph with $n$ vertices and $m$ edges. A configuration is an assignment of one of two colors, black or white, to each edge of $X.$ A move applied to a configuration is to select a black edge…

Inversion sequences, also known as subexcedant sequences, form a fundamental class of objects in enumerative combinatorics. In this paper, we study the joint distribution of five statistics on inversion sequences. While several statistics…

A pair of complex-conjugate fixed points that lie close to the real axis generates a large mass hierarchy in the real renormalization group flow that passes in between them. We show that pairs of complex fixed points that are close to the…

We give direct bijective proofs of the symmetry of the distributions of the number of ascents and descents over standard Young tableaux of shape $\lambda$, where $\lambda$ is a rectangle $(n,n,\dots,n)$ or a truncated staircase…

We generalize the main result of arXiv:2505.17960 and show the consistency of the statement ``There are exactly $n$ $Q$-points up to isomorphism" for any finite $n$. Furthermore, we show that the above statement for $n=2$ can alternatively…

We use three seminal approaches in the study of fixed point theory, the so called $G$-metrics, multidimensional fixed points and partially ordered spaces. More precisely, we extend known results from the theory of quasi-pseudometric spaces…

A group of bijections G acting on a set X is said with fixed points (abbreviated as gaf from the french "groupe {\`a} points fixes") if any element of G has at least one fixed point in X. The G group is said with a common fixed point…

The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We explore the number of fixed points of this map by a statistical…

A partition of the set $[n]:=\{1,2,\ldots,n\}$ is a collection of disjoint nonempty subsets (or blocks) of $[n]$, whose union is $[n]$. In this paper we consider the following rarely used representation for set partitions: given a partition…

Motivated by analogous results for the symmetric group and compact Lie groups, we study the distribution of the number of fixed vectors of a random element of a finite classical group. We determine the limiting moments of these…

A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern statistics of length at most d. Babson and Steingrimsson classified all Mahonian 3-functions up to trivial bijections and…