A closer look at lattice points in rational simplices.
A closer look at some new identities.
A cluster expansion formula ( case).
A co-ideal based identity-summand graph of a commutative semiring
Let be a strong co-ideal of a commutative semiring with identity. Let be a graph with the set of vertices for some , where two distinct vertices and are adjacent if and only if . We look at the diameter and girth of this graph. Also we discuss when is bipartite. Moreover, studies are done on the planarity, clique, and chromatic number of this graph. Examples illustrating the results are presented.
A colorful involution for the generating function for signed Stirling numbers of the first kind.
A color-to-spin domino Schensted algorithm.
A combinatorial approach to evaluation of reliability of the receiver output for BPSK modulation with spatial diversity.
A combinatorial approach to hyperharmonic numbers.
A combinatorial approach to partitions with parts in the gaps
Many links exist between ordinary partitions and partitions with parts in the “gaps”. In this paper, we explore combinatorial explanations for some of these links, along with some natural generalizations. In particular, if we let be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let be the number of partitions of n into j parts where each part is ≡ k (mod m) with parts of size k in the gaps, then .
A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain.
A combinatorial bijection between standard Young tableaux and reduced words of Grassmannian permutations.
A combinatorial characterization of 4-dimensional handlebodies.
A combinatorial derivation of the number of labeled forests.
A combinatorial derivation of the PASEP stationary state.
A combinatorial derivation with Schröder paths of a determinant representation of Laurent biorthogonal polynomials.
A combinatorial formula for orthogonal idempotents in the 0-Hecke algebra of the symmetric group.
A combinatorial formula for the Hilbert series of bigraded -modules.
A combinatorial identity arising from cobordism theory.
A combinatorial inequality. (Eine kombinatorische Ungleichung.)
A combinatorial interpretation for a super-Catalan recurrence.