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SUMMARY:Benjamin Jany (University of Kentucky)
DTSTART:20230406T141500Z
DTEND:20230406T160000Z
DTSTAMP:20260422T070133Z
UID:CJCS/109
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/109/">T
 he direct sum of q-matroids and their decomposition into irreducible compo
 nents</a>\nby Benjamin Jany (University of Kentucky) as part of Copenhagen
 -Jerusalem Combinatorics Seminar\n\n\nAbstract\n$q$-Matroids\, the $q$-ana
 logue of matroids\, have been intensively studied in recent years in codin
 g theory due to their close connection with rank metric codes. In fact\, i
 t was shown in 2018 by Jurrius and Pellikaan that a rank metric code induc
 es a $q$-matroid that captures many of the code's invariants. Many results
  from classical matroid theory were found to have natural $q$-analogues. O
 ne of the major differences between classical matroids and $q$-matroids\, 
 however\,  arose with the introduction of the direct sum of $q$-matroids. 
 In this talk\, I will discuss several combinatorial and algebraic properti
 es of the direct sum of $q$-matroids and show how they differ from the pro
 perties established for classical matroids. I will first show that similar
 ly to matroids\,  $q$-matroids can be decomposed uniquely (up to equivalen
 ce) into the direct sum of irreducible components. However\, we will see t
 hat this result cannot be achieved via a natural analogue of the matroid n
 otion of connected components.  I will then discuss the representability o
 f the direct sum of $q$-matroids. A $q$-matroid is said to be representabl
 e if it is induced by a rank metric code. I will show that unlike classica
 l matroids\, the direct sum of $q$-matroids does not necessarily preserve 
 representability.\n
LOCATION:https://researchseminars.org/talk/CJCS/109/
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