Related papers: Stack-Sorting, Set Partitions, and Lassalle's Sequ…

Valid hook configurations are combinatorial objects used to understand West's stack sorting map as well as cumulants in noncommutative probability theory. We show a bijection between reduced valid hook configurations on 312-avoiding…

We introduce the stack-sorting map $\text{SC}_\sigma$ that sorts, in a right-greedy manner, an input permutation through a stack that avoids some vincular pattern $\sigma$. The stack-sorting maps of Cerbai et al. in which the stack avoids a…

This paper is devoted to the study of the log-convexity of combinatorial sequences. We show that the log-convexity is preserved under componentwise sum, under binomial convolution, and by the linear transformations given by the matrices of…

In the paper, the authors present several new relations and applications for the combinatorial sequence that counts the possible partitions of a finite set with the restriction that the size of each block is contained in a given set. One of…

We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number…

In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…

We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…

Defant, Engen, and Miller defined a refinement of Lassalle's sequence $A_{k+1}$ by considering uniquely sorted permutations of length $2k+1$ whose first element is $\ell$. They showed that each such sequence is symmetric in $\ell$ and…

In this work of thesis we introduce and study a new family of sorting devices, which we call pattern-avoiding machines. They consist of two stacks in series, equipped with a greedy procedure. On both stacks we impose a static constraint in…

The Delta Conjecture of Haglund, Remmel, and Wilson is a recent generalization of the Shuffle Conjecture in the field of diagonal harmonics. In this paper we give evidence for the Delta Conjecture by proving a pair of conjectures of Wilson…

In 2012 Jan Saxl conjectured that all irreducible representations of the symmetric group occur in the decomposition of the tensor square of the irreducible representation corresponding to the staircase partition. We make progress on this…

Following the footprints of what have been done with the algorithm Stacksort, we investigate the preimages of the map associated with a slightly less well known algorithm, called Queuesort. After having described an equivalent version of…

We consider sorting procedures for permutations making use of pop stacks with a bypass operation, and explore the combinatorial properties of the associated algorithms.

Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of…

We consider uniformly random set partitions of size $n$ with exactly $k$ blocks, and uniformly random permutations of size $n$ with exactly $k$ cycles, under the regime where $n-k \sim t\sqrt{n}$, $t>0$. In this regime, there is a simple…

For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $\Pi^{\bullet}_{\vec{c}}$ is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with…

Using the ring space of sheared Witt vectors, we define certain ring stacks. We suggest several models for the ring stacks. Motivation: there is a conjectural description of the stack of n-truncated Barsotti-Tate groups and its Shimurian…

In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…

We investigate partitioning of integer sequences into heapable subsequences (previously defined and established by Mitzenmacher et al). We show that an extension of patience sorting computes the decomposition into a minimal number of…

We prove a partition identity conjectured by Lassalle (Adv. in Appl. Math. 21 (1998), 457-472).