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Introduction
My primary research focus lies in Enumerative Combinatorics, a field that delves into the systematic counting and arrangement of discrete structures. I am particularly intrigued by the intricate patterns and relationships that emerge within combinatorial structures. Moreover, I am dedicated to exploring the intersections of Enumerative Combinatorics with other branches of mathematics, with a keen interest in uncovering connections to both algebra and analysis
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Publications
Publications (7)
The $(P, w)$-partition generating function $K_{(P,w)}(x)$ is a quasisymmetric function obtained from a labeled poset. Recently, Liu and Weselcouch gave a formula for the coefficients of $K_{(P,w)}(x)$ when expanded in the quasisymmetric power sum function basis. This formula generalizes the classical Murnaghan--Nakayama rule for Schur functions. We...
We study a sorting procedure (run-sorting) on permutations, where runs are rearranged in lexico-graphic order. We describe a rather surprising bijection on permutations on length n, with the property that it sends the set of peak-values (also known as the pinnacle set) to the set of peak-values after run-sorting. We also prove that the expected num...
We study a sorting procedure (run-sorting) on permutations, where runs are rearranged in lexicographic order. We describe a rather surprising bijection on permutations on length $n$, with the property that it sends the set of peak-values to the set of peak-values after run-sorting. We also prove that the expected number of descents in a permutation...
The study of pattern avoidance in permutations, and specifically in flattened partitions is an active area of current research. In this paper, we count the number of distinct flattened partitions over [n] avoiding a single pattern, as well as a pair of two patterns. Several counting sequences, namely Catalan numbers, powers of two, Fi-bonacci numbe...
The study of pattern avoidance in permutations, and specifically in flattened partitions is an active area of current research. In this paper, we count the number of distinct flattened partitions over [n] avoiding a single pattern, as well as a pair of two patterns. Several counting sequences, namely Catalan numbers, powers of two, Fibonacci number...
The study of flattened partitions is an active area of current research. In this paper, our study unexpectedly leads us to the OEIS sequence A124324. We provide a 1 Corresponding author. 1 new combinatorial interpretation of these numbers. A combinatorial bijection between flattened partitions over [n + 1] and the partitions of [n] is also given in...
The study of flattened partitions is an active area of current research. In this paper, our study unexpectedly leads us to the OEIS numbers A124324. We provide a new combinatorial interpretation of these numbers. A combinatorial bijection between flattened partitions over $[n+1]$ and the partitions of $[n]$ is also given in a separate section. We i...
