Together with a characteristic function, idempotent permutations uniquely determine idempotent maps, as well as their linearly ordered arrangement simultaneously. Furthermore, in-place linear time transformations are possible between them. Hence, they may be important for succinct data structures, information storing, sorting and searching. In this study, their combinatorial interpretation is g...

begin{abstract} the relations between the spectrum of the matrix $q+r$ and the spectra of the matrices $(gamma + delta)q+(alpha + beta)r-qr-rq$, $qr-rq$, $alpha beta r-qrq$, $alpha rqr-(qr)^{2}$, and $beta r-qr$ have been given on condition that the matrix $q+r$ is diagonalizable, where $q$, $r$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $...

Because they play a role in our understanding of the symmetric group algebra, Lie idempotents have received considerable attention. The Klyachko idempotent has attracted interest from combinatorialists, partly because its definition involves the major index of permutations. For the symmetric group Sn, we look at the symmetric group algebra with coefficients from the field of rational functions ...

One-parameter semigroups of antitriangle idempotent supermatrices and corresponding superoperator semigroups are introduced and investigated. It is shown that t-linear idempotent superoperators and exponential superoperators are mutually dual in some sense, and the first gives additional to exponential solution to the initial Cauchy problem. The corresponding functional equation and analog of r...

A game is considered where the communication network of the first player is explicitly modeled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modeled through expectations over idempotent probability measures. The idempotent probabilities are conditioned by observational data, the arrival of which may have been delayed along th...

Machine checked proofs of type inference algorithms often axiomatize MGU behavior as a set of axioms. Idempotent MGUs for a list of equational constraints are needed to reason about the correctness of Wand’s type inference algorithm and our extension of it. To characterize the behavior of idempotent MGUs, we propose a set of seven axioms; four of which have been proven in our earlier paper, whe...