arXiv subjects

Yunseo Choi

Publications and source records attributed to Yunseo Choi.

10 recordsLinked to original sources

arXiv2026

InnerPond: Fostering Inter-Self Dialogue with a Multi-Agent Approach for Introspection

Introspection is central to identity construction and future planning, yet most digital tools approach the self as a unified entity. In contrast, Dialogical Self Theory (DST) views the self as composed of multiple internal perspectives, such as values, concerns, and aspirations, that can come into tension or dialogue with one another. Building on this view, we designed InnerPond, a research probe in the form of a multi-agent system that represents these internal perspectives as distinct LLM-based agents for introspection. Its design was shaped through iterative explorations of spatial metaphors, interaction scaffolding, and conversational orchestration, culminating in a shared spatial environment for organizing and relating multiple inner perspectives. In a user study with 17 young adults navigating career choices, participants engaged with the probe by co-creating inner voices with AI, composing relational inner landscapes, and orchestrating dialogue as observers and mediators, offering insight into how such systems could support introspection. Overall, this work offers design implications for AI-supported introspection tools that enable exploration of the self's multiplicity.

cs.HC↗

arXiv2024

Ungar Games on the Young-Fibonacci and the Shifted Staircase Lattices

In 2023, Defant and Li introduced the Ungar move, which sends an element $v$ of a finite meet-semilattice $L$ to the meet of some subset of the elements covered by $v$. More recently, Defant, Kravitz, and Williams introduced the Ungar game on $L$, in which two players take turns making Ungar moves starting from an element of $L$ until the player that cannot make a nontrivial Ungar move loses. In this note, we settle two conjectures by Defant, Kravitz, and Williams on the Ungar games on the Young-Fibonacci lattice and the lattices of the order ideals of shifted staircases.

math.CO↗

arXiv2024

On the set partitions that require maximum sorts through the $aba-$avoiding stack

Recently, Xia introduced a deterministic variation $ϕ_σ$ of Defant and Kravitz's stack-sorting maps for set partitions and showed that any set partition $p$ is sorted by $ϕ^{N(p)}_{aba}$, where $N(p)$ is the number of distinct alphabets in $p$. Xia then asked which set partitions $p$ are not sorted by $ϕ_{aba}^{N(p)-1}$. In this note, we prove that the minimal length of a set partition $p$ that is not sorted by $ϕ_{aba}^{N(p)-1}$ is $2N(p)$. Then we show that there is only one set partition of length $2N(p)$ and ${{N(p) + 1} \choose 2} + 2{N(p) \choose 2}$ set partitions of length $2N(p)+1$ that are not sorted by $ϕ_{aba}^{N(p)-1}$.

math.CO↗

arXiv2023

Tamagawa Products for Elliptic Curves Over Number Fields

In recent work, Griffin, Ono, and Tsai constructs an $L-$series to prove that the proportion of short Weierstrass elliptic curves over $\mathbb{Q}$ with trivial Tamagawa product is $0.5054\dots$ and that the average Tamagawa product is $1.8183\dots$. Following their work, we generalize their $L-$series over arbitrary number fields $K$ to be \[L_{\mathrm{Tam}}(K; s):=\sum_{m=1}^{\infty}\frac{P_{\mathrm{Tam}}(K; m)}{m^s},\] where $P_{\mathrm{Tam}}(K;m)$ is the proportion of short Weierstrass elliptic curves over $K$ with Tamagawa product $m$. We then construct Markov chains to compute the exact values of $P_{\mathrm{Tam}}(K;m)$ for all number fields $K$ and positive integers $m$. As a corollary, we also compute the average Tamagawa product $L_{\mathrm{Tam}}(K;-1)$. We then use these results to uniformly bound $P_{\mathrm{Tam}}(K;1)$ and $L_{\mathrm{Tam}}(K,-1)$ in terms of the degree of $K$. Finally, we show that there exist sequences of $K$ for which $P_{\mathrm{Tam}}(K;1)$ tends to $0$ and $L_{\mathrm{Tam}}(K;-1)$ to $\infty$, as well as sequences of $K$ for which $P_{\mathrm{Tam}}(K;1)$ and $L_{\mathrm{Tam}}(K;-1)$ tend to $1$.

math.NT↗

arXiv2023

On a conjecture on pattern-avoiding machines

Let $s$ be West's stack-sorting map, and let $s_{T}$ be the generalized stack-sorting map, where instead of being required to increase, the stack avoids subpermutations that are order-isomorphic to any permutation in the set $T$. In 2020, Cerbai, Claesson, and Ferrari introduced the $σ$-machine $s \circ s_σ$ as a generalization of West's $2$-stack-sorting-map $s \circ s$. As a further generalization, in 2021, Baril, Cerbai, Khalil, and Vajnovski introduced the $(σ, τ)$-machine $s \circ s_{σ, τ}$ and enumerated $|\Sort_{n}(σ,τ)|$ -- the number of permutations in $S_n$ that are mapped to the identity by the $(σ, τ)$-machine -- for six pairs of length $3$ permutations $(σ, τ)$. In this work, we settle a conjecture by Baril, Cerbai, Khalil, and Vajnovski on the only remaining pair of length $3$ patterns $(σ, τ) = (132, 321)$ for which $|\Sort_{n}(σ, τ)|$ appears in the OEIS. In addition, we enumerate $|\Sort_n(123, 321)|$, which does not appear in the OEIS, but has a simple closed form.

math.CO↗

arXiv2022

The Image of the Pop Operator on Various Lattices

Extending the classical pop-stack sorting map on the lattice given by the right weak order on $S_n$, Defant defined, for any lattice $M$, a map $\mathsf{Pop}_{M}: M \to M$ that sends an element $x\in M$ to the meet of $x$ and the elements covered by $x$. In parallel with the line of studies on the image of the classical pop-stack sorting map, we study $\mathsf{Pop}_{M}(M)$ when $M$ is the weak order of type $B_n$, the Tamari lattice of type $B_n$, the lattice of order ideals of the root poset of type $A_n$, and the lattice of order ideals of the root poset of type $B_n$. In particular, we settle four conjectures proposed by Defant and Williams on the generating function \begin{equation*} \mathsf{Pop}(M; q) = \sum_{b \in \mathsf{Pop}_{M}(M)} q^{|\mathscr{U}_{M}(b)|}, \end{equation*} where $\mathscr{U}_{M}(b)$ is the set of elements of $M$ that cover $b$.

math.CO↗

arXiv2022

Counting crucial permutations with respect to monotone patterns

Recently, Avgustinovich, Kitaev, and Taranenko defined five types of $(k, \ell)-$crucial permutations, which are maximal permutations that do not contain an increasing subsequence of length $k$ or a decreasing subsequence of length $\ell$. Further, Avgustinovich, Kitaev, and Taranenko began the enumeration of the $(k, \ell)-$crucial permutations of the minimal length and the next minimal length and the $(k, 3)-$crucial permutations of all lengths for each of the five types of $(k,\ell)-$crucial permutations. In this paper, we complete the enumeration that Avgustinovich, Kitaev, and Taranenko began.

math.CO↗

arXiv2021

Congruences in fractional partition functions

The coefficients of the generating function $(q;q)^α_\infty$ produce $p_α(n)$ for $α\in \mathbb{Q}$. In particular, when $α= -1$, the partition function is obtained. Recently, Chan and Wang identified and proved congruences of the form $p_{\frac{a}{b}}(\ell n + c)\equiv 0 \pmod{\ell}$ where $\ell$ is a prime such that $\ell \mid a -db$ for $d \in \{4, 6, 8, 10, 14, 26\}$. Expanding upon their work, we use the representation of powers of the Dedekind-eta functions in linear sums of Hecke eigenforms and their lacunarity to raise the power of the modulus to higher powers of $\ell$. In addition, we generate congruences for when $d=2$ employing Hecke algebra.

math.NT↗

arXiv2020

Racial Impact on Infections and Deaths due to COVID-19 in New York City

Redlining is the discriminatory practice whereby institutions avoided investment in certain neighborhoods due to their demographics. Here we explore the lasting impacts of redlining on the spread of COVID-19 in New York City (NYC). Using data available through the Home Mortgage Disclosure Act, we construct a redlining index for each NYC census tract via a multi-level logistical model. We compare this redlining index with the COVID-19 statistics for each NYC Zip Code Tabulation Area. Accurate mappings of the pandemic would aid the identification of the most vulnerable areas and permit the most effective allocation of medical resources, while reducing ethnic health disparities.

q-bio.PE↗

arXiv2019

Ramanujan Congruences for Fractional Partition Functions

For rational $α$, the fractional partition functions $p_α(n)$ are given by the coefficients of the generating function $(q;q)^α_\infty$. When $α=-1$, one obtains the usual partition function. Congruences of the form $p(\ell n + c)\equiv 0 \pmod{\ell}$ for a prime $\ell$ and integer $c$ were studied by Ramanujan. Such congruences exist only for $\ell\in\{5,7,11\}.$ Chan and Wang [4] recently studied congruences for the fractional partition functions and gave several infinite families of congruences using identities of the Dedekind eta-function. Following their work, we use the theory of non-ordinary primes to find a general framework that characterizes congruences modulo any integer. This allows us to prove new congruences such as $p_\frac{57}{61}(17^2n-3)\equiv 0 \pmod{17^2}$.

math.NT↗