Let K[HKΘ] denote the Hecke–Kiselman algebra of a finite oriented graph Θ over an algebraically closed field K. All irreducible representations, and corresponding maximal ideals K[HKΘ], are characterized in case this satisfies polynomial identity. The latter condition corresponds to simple that can be expressed terms Θ. result shows surprising similarity classical results on representations sem...

In general semimodules, we say that the image of a linear operator B and the kernel of a linear operator C are direct factors if every equivalence class modulo C crosses the image of B at a unique point. For linear maps represented by matrices over certain idempotent semifields such as the (max,+)-semiring, we give necessary and sufficient conditions for an image and a kernel to be direct facto...

In this paper we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to Laffey ([12]) and Rao ([3]) to noncommutative setting and fill in the gaps in the original proof of Rao’s main theorems (cf. [3], Theorems 5 and 7 and [4]). We a...

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...

Labelling Neural Matrix and Collective Dynamics Mau-Hsiang Shih 施茂祥 National Normal University, Taiwan Email: [email protected] Abstract The brain is considered to be a complex, self-organizing system; it consists of enormous numbers of interacting neurons and perpetually weaves its intricate web. Scientists believe that collective dynamics of the brain is deeply entwined with the neural ...

Idempotent mathematics is based on replacing the usual arithmetic operations with a new set of basic operations, that is on replacing numerical fields by idempotent semirings. Exotic semirings such as the max-plus algebra Rmax or concatenation semiring P(Σ) have been introduced in connection with various fields: graph theory, Markov decision processes, language theory, discrete event systems th...

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...