Incidence Algebras

The floor quotient partial order

“…is the set of Z-valued functions on the set of pairs (d, n) such that d ≼ 1 n under the operations of addition and convolution, see Smith [10,11]. For general structures of incidence algebras over a ring R, which are in general non-commutative associative algebras, see Stanley [13] and Spiegel and O'Donnell [12]. In general, zeta functions and Möbius functions of (locally finite) partial orders are members of the incidence algebra.…”

Derivations of Incidence Algebras

“…This paper is devoted to the derivations of the incidence algebra I(X, R) for an arbitrary preordered set X and an arbitrary algebra R over some commutative ring T. The initial stage of research into the derivations of incidence rings can be found in the book [15]. The final result of this stage is Theorem 7.1.4 [15].…”

“…This paper is devoted to the derivations of the incidence algebra I(X, R) for an arbitrary preordered set X and an arbitrary algebra R over some commutative ring T. The initial stage of research into the derivations of incidence rings can be found in the book [15]. The final result of this stage is Theorem 7.1.4 [15]. It describes the derivations of the R-algebra I(X, R), where X is a partially ordered set and R is a commutative ring (see Corollary 6 of the given paper).…”

“…Over time, incidence algebras themselves, regardless of their applications in combinatorics and other areas of mathematics, have turned out to be a meaningful algebraic object. Many works are dedicated to them, including the book [15].…”

A Categorical Approach to Statistical Mechanics

“…For a given poset A , we call such representation an A -specification. Representations of posets have a precise geometric interpretation [33][34][35][36][37], and there is a rich literature coming from algebra, geometry, and topology to study them. We showed that phases of statistical systems are geometric invariants of these representations and computed them for 'projective' poset representations.…”