arXiv subjects

Samuel Ramírez

Publications and source records attributed to Samuel Ramírez.

3 recordsLinked to original sources

arXiv2026

Fibonacci and Catalan Numbers Meet in Staircase Polyominoes

We study Fibonacci (staircase) polyominoes, a class of column-convex polyominoes whose lower boundary is a staircase with unit vertical steps. We derive multivariate generating functions that refine Turban's Fibonacci-number enumeration by tracking additional perimeter and area parameters. The proofs use a catalytic functional equation and, in a perimeter specialization, the kernel method, leading to explicit closed forms and Catalan-number coefficient formulas.

cs.DM↗

arXiv2025

Restricted Fubini Rankings and Restricted Unit Interval Parking Functions

We study three natural types of restrictions on Fubini rankings and unit interval parking functions, which are motivated by their correspondence with ordered set partitions. For each restriction type, we define the corresponding subset of Fubini rankings and unit interval parking functions, establish enumerative results, and provide bijections between the restricted families. We also obtain exponential generating functions and combinatorial interpretations, including connections with exceedances in permutations and with the absence of cyclical adjacencies in set partitions.

math.CO↗

arXiv2025

Lucky Cars in Fubini Rankings and Unit Fubini Rankings

We study lucky cars in subsets of parking functions, called Fubini rankings and unit Fubini rankings. A Fubini ranking is a sequence of nonnegative integers that encodes a valid ranking of competitors, where ties are allowed. A car (or competitor) is said to be lucky if it is the first instance of that rank appearing in the sequence. We present combinatorial characterizations and enumeration formulas for lucky cars in both Fubini rankings and unit Fubini rankings, and establish connections between these objects and ordered set partitions, as well as integer compositions. To obtain our results, we use several techniques to enumerate statistics over these families of objects. In particular, we employ generating functions, bijective and combinatorial arguments, recurrence relations, and Zeilberger's creative telescoping method.

math.CO↗