R. Stanley

activity

19972023

most citedA conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group

31 citations · 158 across the 54 of their papers we have counts for

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56 papers · 1 filter

math.CO2023★ 1 cited

The Redei--Berge symmetric function of a directed graph

Darij Grinberg, Richard P. Stanley

Let $D = (V, A)$ be a digraph with $n$ vertices, where each arc $a \in A$ is a pair $(u, v)$ of two vertices. We study the \emph{Redei--Berge symmetric functio…

math.CO2023

Some enumerative properties of parking functions

Richard P. Stanley, Mei Yin

A parking function is a sequence $(a_{1}, \dots, a_{n})$ of positive integers such that if $b_{1} \leq \dots \leq b_{n}$ is the increasing rearrangement of $a_{1}, \dots, a_{n}$ , then $b_{i} \leq i$ f…

math.CO2023

Posets of width two and skew Young diagrams

Richard P. Stanley

Let $P$ be a finite poset of width two, i.e., with no three-element antichain. We associate with $P$ a skew Young diagram $Υ (P)$ and discuss some of the properties of the map $Υ$ .…

math.CO2021★ 1 cited

Theorems and Conjectures on Some Rational Generating Functions

Richard P. Stanley

Let $I_{n} (x) = \prod_{i = 1}^{n} (1 + x^{F_{i + 1}})$ , where $F_{i + 1}$ denotes a Fibonacci number. Let $v_{r} (n)$ denote the sum of the $r$ th powers of the coefficients of $I_{n} (x)$ .…

math.CO2019

Some Linear Recurrences Motivated by Stern's Diatomic Array

Richard P. Stanley

We define a triangular array closely related to Stern's diatomic array and show that for a fixed integer $r \geq 1$ , the sum $u_{r} (n)$ of the $r$ th powers of the entries in row $n$ s…

math.CO2017

A generalization of a 1998 unimodality conjecture of Reiner and Stanton

Richard P. Stanley, Fabrizio Zanello

An interesting, and still wide open, conjecture of Reiner and Stanton predicts that certain "strange" symmetric differences of $q$ -binomial coefficients are always nonnegative and…