Using the correspondence between alternating permutations and pairs of matchings, we present a combinatorial proof for the enumeration of alternating permutations with given peak set. Moreover, we give a refinement according to the number of left to right maxima.

Stereoisograms of octahedral complexes are classified into five types (type I--typeV) under the action of the corresponding RS-stereoisomeric group. Their enumeration is accomplished in a type-itemized fashion, where Fujita's proligand method developed originally for combinatorial enumeration under point groups (S. Fujita, Theor. Chem. Acc., 113, 73--79 (2005)) is extended to meet the requireme...

Hochschild lattices are specific intervals in the dexter meet-semilattices recently introduced by Chapoton. A natural geometric realization of these leads to some cell complexes Saneblidze, called polytopes. We obtain several geometrical properties lattices, namely we give cubic realizations, establish that EL-shellable, and show they constructible interval doubling. also prove combinatorial as...

Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence we deduce the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproducts are a purely combinatorial algorithm to describe the irreducible decomposition of the tensor product of two irreducible representations of the symmetric group, and...

Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures. “Singularity analysis” reviewed here provides constructive estimates that are applicable in several areas...

Systems of functional equations for generating functions appear in many combinatorial enumeration problems, for example in tree enumeration problems or in the enumeration of planar graphs (and related problems), see Drmota (2009). Usually, these enumeration techniques can be extended to take several parameters into account: the number of vertices, the number of edges, the number of vertices of ...

The refined enumeration of alternating sign matrices (ASMs) of given order having prescribed behavior near one or more of their boundary edges has been the subject of extensive study, starting with the Refined Alternating Sign Matrix Conjecture of Mills-Robbins-Rumsey [25], its proof by Zeilberger [31], and more recent work on doublyrefined and triply-refined enumeration by several authors. In ...

The q-semicircular distribution is a probability law that interpolates between the Gaussian law and the semicircular law. There is a combinatorial interpretation of its moments in terms of matchings where q follows the number of crossings, whereas for the free cumulants one has to restrict the enumeration to connected matchings. The purpose of this article is to describe combinatorial propertie...

We present a general step-by-step extending approach to parallel execution of enumeration of combinatorial objects (ECO).Themethodology extends a famous enumeration algorithm,OrderlyGeneration, which allows concurrently generating all objects of size n + 1 from all objects of size n. To the best of our knowledge, this is the first time there is an attempt to plug parallel computing into Orderly...

stereoisograms of octahedral complexes are classified into five types (type i--typev) under the action of the corresponding rs-stereoisomeric group. their enumeration is accomplished in a type-itemized fashion, where fujita's proligand method developed originally for combinatorial enumeration under point groups (s. fujita, theor. chem. acc., 113, 73--79 (2005)) is extended to meet the requireme...