Meeting Menu

2026 Fall Meeting – Student Posters

Utica University

Saturday – Oct 24

Location: Library Concourse

  1. Time:
    3:30 pm – 4:00 pm
    Title:
    Pattern Avoidance in Lattice and Yamanouchi Words
    Speakers:
    Alanna Pellicane (SUNY Brockport), Rebecca Smith (SUNY Brockport)
    Abstract

    This research focuses on pattern avoidance in binary lattice and Yamanouchi words. A lattice word (sometimes referred to as a ballot sequence) when read from left to right always has at least as many entries of value $i$ as it has of value $i+1$. These words were noted by Mark Dukes as being ascent sequences. A Yamanouchi word is a reversed lattice word. For each pattern $w$ of size three, we determine the number of binary Yamanouchi words of size $n$ that avoid $w$.

  2. Time:
    3:30 pm – 4:00 pm
    Title:
    Generalizations of the Classical Gaussian Integral
    Speaker:
    Asim Nepal (SUNY Brockport)
    Abstract

    The classical Gaussian integral is a fundamental result in analysis, probability, and statistics, but it represents only one member of a broader family of improper integrals. This project investigates what happens when its fixed quadratic exponent is replaced by a positive parameter. Specifically, we study \[ I(n)=\int_0^\infty e^{-x^n}\,dx,\qquad n > 0, \] with the goal of determining when the integral converges, finding an exact formula for its value, and understanding how the area under $e^{-x^n}$ changes as $n$ varies. Using the substitution $t=x^n$ and properties of the Gamma function, we obtain \[ I(n)=\Gamma\left(1+\frac{1}{n}\right). \] We then analyze this expression with respect to $n$ and show that $I(n)$ converges for every $n > 0$. Rather than changing monotonically, the area decreases to a unique minimum at approximately $n=2.16623$ and then increases toward $1$ as $n\to\infty$, while $I(n)\to\infty$ as $n\to0^+$. We also extend the same Gamma-function approach to weighted and scaled Gaussian-type integrals. Finally, composite Trapezoidal and Simpson's Rules are used to compare numerical approximations with exact values and to distinguish quadrature error from truncation error. Overall, the project shows how varying a single exponent transforms the classical Gaussian integral into a broader family with an exact analytic structure and predictable numerical behavior.

  3. Time:
    3:30 pm – 4:00 pm
    Title:
    Cards on the Table: The Winning Move Is Not in the Rules
    Speaker:
    Jack Lamberg (Binghamton University)
    Abstract

    Playing a collectible card game well takes more than following the rules. A strong player must perceive the visible board, know which moves are legal, recall what has been played, reason about hidden information, and judge which legal move is best. In these games, individual card effects take precedence over the base rules, so the winning move usually cannot be deduced from the rulebook alone. We introduce Cards on the Table, a benchmark that probes these abilities in language models (LLMs) and vision-language models (VLMs). It is built on Aurora’s Call, a purpose-built two-player card game whose deterministic engine provides exact ground truth and the full set of legal moves for any state. From recorded games, we automatically generate engine-verified questions in seven categories: perception, move legality, illegal-action diagnosis, public-card tracking, resource reasoning, state-change prediction, and replay reasoning, each posed in matched text (LLM) and image (VLM) form, and we complement the question benchmark with full-game play against scripted bots. Across five open models (Qwen2.5, Llama 3.1, Qwen2.5-VL, InternVL3, and LLaVA-OneVision), the best model answers only 57.5% of questions correctly, with counterfactual resource arithmetic below 40% for every model; in full games, models beat a random-move bot but lose the large majority of games to simple scripted heuristics that a human defeats 100% of the time. We further outline a memory-augmented agent that accumulates card knowledge across games to re-rank moves.

  4. Time:
    3:30 pm – 4:00 pm
    Title:
    Sub Cesaro Operators
    Speaker:
    Luke Schneider (SUNY Brockport)
    Abstract

    Sub Cesaro operators are projections of the classical Cesaro operators on some subspaces. They were introduced in 2024 in conjunction with the problem of the boundedness of the Rhaly matrices. Except for some very simple cases the general theory of Rhaly matrices does not apply for this kind of operators. We will discuss their norms, eigenvalues, spectral properties in general, compactness, membership in Schatten ideals and other properties.