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BEGIN:VEVENT
UID:87cf4fc68c98c9311493107ad08a6272
CATEGORIES:Symmetric Functions & Probability Theory Seminar
CREATED:20250304T102404
SUMMARY:The generalized Pitman-Stanley flow polytope
LOCATION:Hill 705
DESCRIPTION:Date: 03/26/2025Speaker: Alejandro Morales (https://sites.google.com/view/a
 hmorales/) (Montreal)\nTitle: The generalized Pitman-Stanley flow polytope\
 nAbstract: In 1999, Pitman and Stanley introduced the polytope bearing thei
 r name along with a study of its faces, lattice points, and volume. This po
 lytope is well-studied due to its connections to parking functions, lattice
  path matroids, generalized permutahedra/polymatroids, and flow polytopes. 
 Its lattice points correspond to plane partitions of skew shape with entrie
 s 0 and 1. Pitman and Stanley remarked that their polytope can be generaliz
 ed so that lattice points correspond to plane partitions of skew shape with
  entries 0,1,...,m. Since then, this generalization has been untouched. We 
 study this polytope and show that it can also be realized as a flow polytop
 e of a grid graph. In this talk I will discuss characterizations of its ver
 tices and give formulas for the number of vertices and faces as well as old
  and new formulas for the number of lattice points and volume in terms of r
 ectangular Standard Young Tableaux. The new formulas come from the volume p
 olynomial formulas of flow polytopes in terms of vector partition functions
  of Baldoni and Vergne and lattice point formulas of Stanley of marked orde
 r polytopes.\nThis is joint work with Maura Hegarty, William Dugan, and Ann
 ie Raymond.\n
X-ALT-DESC;FMTTYPE=text/html:<div jscontroller="Ae65rd" jsaction="https://math.rutgers.edu/touchstart:Ur
 sOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rj
 c:jbFSOd;CrfLRd:SzACGe;" style="display: inline-block; max-width: 100%; pos
 ition: relative;"><span style="font-family: Lato, Arial; font-size: 11pt; f
 ont-variant: normal; font-weight: bold; vertical-align: baseline;">Date</sp
 an><span style="font-size: 11pt; font-variant: normal; vertical-align: base
 line;">: 03/</span><span style="font-size: 11pt; vertical-align: baseline;"
 >26</span><span style="font-size: 11pt; font-variant: normal; vertical-alig
 n: baseline;">/2025</span></div><p dir="ltr" style="margin: 12px 0px 0px; o
 utline: none; position: relative; color: #212121; font-size: 11pt; font-sty
 le: normal; font-weight: 400; font-family: Lato, sans-serif; line-height: 1
 .6667; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 
 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: norma
 l;"><span style="font-family: Lato, Arial; font-variant: normal; font-weigh
 t: bold;">Speaker</span><span style="font-variant: normal;">:&nbsp;</span><
 a href="https://sites.google.com/view/ahmorales/" target="_blank" rel="noop
 ener" style="color: inherit; text-decoration: none;"><span style="color: #0
 06580; text-decoration: underline;">Alejandro Morales</span></a>&nbsp;(Mont
 real)</p><p dir="ltr" style="margin: 12px 0px 0px; outline: none; position:
  relative; color: #212121; font-size: 11pt; font-style: normal; font-weight
 : 400; font-family: Lato, sans-serif; line-height: 1.6667; letter-spacing: 
 normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: no
 ne; widows: 2; word-spacing: 0px; white-space: normal;"><span style="font-f
 amily: Lato, Arial; font-variant: normal; font-weight: bold;">Title</span><
 span style="font-variant: normal;">:&nbsp;</span>The generalized Pitman-Sta
 nley flow polytope</p><p dir="ltr" style="margin: 12px 0px 0px; outline: no
 ne; position: relative; color: #212121; font-size: 11pt; font-style: normal
 ; font-weight: 400; font-family: Lato, sans-serif; line-height: 1.6667; let
 ter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-
 transform: none; widows: 2; word-spacing: 0px; white-space: normal;"><span 
 style="font-family: Lato, Arial; font-variant: normal; font-weight: bold;">
 Abstract</span><span style="font-variant: normal;">:&nbsp;</span>In 1999, P
 itman and Stanley introduced the polytope bearing their name along with a s
 tudy of its faces, lattice points, and volume. This polytope is well-studie
 d due to its connections to parking functions, lattice path matroids, gener
 alized permutahedra/polymatroids, and flow polytopes. Its lattice points co
 rrespond to plane partitions of skew shape with entries 0 and 1. Pitman and
  Stanley remarked that their polytope can be generalized so that lattice po
 ints correspond to plane partitions of skew shape with entries 0,1,...,m. S
 ince then, this generalization has been untouched. We study this polytope a
 nd show that it can also be realized as a flow polytope of a grid graph. In
  this talk I will discuss characterizations of its vertices and give formul
 as for the number of vertices and faces as well as old and new formulas for
  the number of lattice points and volume in terms of rectangular Standard Y
 oung Tableaux. The new formulas come from the volume polynomial formulas of
  flow polytopes in terms of vector partition functions of Baldoni and Vergn
 e and lattice point formulas of Stanley of marked order polytopes.</p><p di
 r="ltr" style="margin: 12px 0px 0px; outline: none; position: relative; col
 or: #212121; font-size: 11pt; font-style: normal; font-weight: 400; font-fa
 mily: Lato, sans-serif; line-height: 1.6667; padding-bottom: 0px; letter-sp
 acing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transf
 orm: none; widows: 2; word-spacing: 0px; white-space: normal;">This is join
 t work with Maura Hegarty, William Dugan, and Annie Raymond.</p>
CONTACT:Alejandro Morales 
DTSTAMP:20260829T213127
DTSTART;TZID=America/New_York:20250326T104500
DTEND;TZID=America/New_York:20250326T234500
SEQUENCE:0
TRANSP:OPAQUE
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