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UID:bfb367d78581f4ecf882b85af89961db
CATEGORIES:Experimental Mathematics Seminar
CREATED:20260205T181330
SUMMARY: Counting Colored Tilings on Grids and Graphs
LOCATION:https://rutgers.zoom.us/j/95103383827    password: 6564120420
DESCRIPTION: In this talk we study a counting problem that originated on Mathematics St
 ack Exchange: How many ways can a rectangular grid be partitioned into a pr
 escribed number of connected polyominoes when the pieces are colored, and a
 ny two pieces that share an edge must have different colors? We organize th
 ese numbers using bivariate generating functions, where one variable record
 s the length of the grid and the other records the number of pieces. Using 
 generating functions, we obtain explicit rational expressions in the first 
 nontrivial cases of two and three rows. We then recast the model in graph-t
 heoretic terms by replacing grids with Cartesian products of a fixed graph 
 and a path, and by counting properly colored partitions into connected bloc
 ks. This leads to analogous generating functions on graphs, including close
 d forms for specific families (such as complete graphs), and to a computati
 onal framework for exploring further examples. This is joint work with Dieg
 o Villamizar (Xavier University of Louisiana\n
X-ALT-DESC;FMTTYPE=text/html:<p>&nbsp;In this talk we study a counting problem that originated on Mathem
 atics Stack Exchange: How many ways can a rectangular grid be partitioned i
 nto a prescribed number of connected polyominoes when the pieces are colore
 d, and any two pieces that share an edge must have different colors? We org
 anize these numbers using bivariate generating functions, where one variabl
 e records the length of the grid and the other records the number of pieces
 . Using generating functions, we obtain explicit rational expressions in th
 e first nontrivial cases of two and three rows. We then recast the model in
  graph-theoretic terms by replacing grids with Cartesian products of a fixe
 d graph and a path, and by counting properly colored partitions into connec
 ted blocks. This leads to analogous generating functions on graphs, includi
 ng closed forms for specific families (such as complete graphs), and to a c
 omputational framework for exploring further examples. This is joint work w
 ith Diego Villamizar (Xavier University of Louisiana</p>
CONTACT: José L. Ramirez, Universidad Nacional de Colombia
DTSTAMP:20260826T145752
DTSTART;TZID=America/New_York:20260212T170000
DTEND;TZID=America/New_York:20260212T180000
SEQUENCE:0
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