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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://www.math.rutgers.edu/touchstar
 t:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;f
 v1Rjc:jbFSOd;CrfLRd:SzACGe;" style="display: inline-block; max-width: 100%;
  position: relative;"><span style="font-family: Lato, Arial; font-size: 11p
 t; font-variant: normal; font-weight: bold; vertical-align: baseline;">Date
 </span><span style="font-size: 11pt; font-variant: normal; vertical-align: 
 baseline;">: 03/</span><span style="font-size: 11pt; vertical-align: baseli
 ne;">26</span><span style="font-size: 11pt; font-variant: normal; vertical-
 align: baseline;">/2025</span></div><p dir="ltr" style="margin: 12px 0px 0p
 x; outline: none; position: relative; color: #212121; font-size: 11pt; font
 -style: normal; font-weight: 400; font-family: Lato, sans-serif; line-heigh
 t: 1.6667; letter-spacing: normal; orphans: 2; text-align: start; text-inde
 nt: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: n
 ormal;"><span style="font-family: Lato, Arial; font-variant: normal; font-w
 eight: bold;">Speaker</span><span style="font-variant: normal;">:&nbsp;</sp
 an><a href="https://sites.google.com/view/ahmorales/" target="_blank" rel="
 noopener" style="color: inherit; text-decoration: none;"><span style="color
 : #006580; text-decoration: underline;">Alejandro Morales</span></a>&nbsp;(
 Montreal)</p><p dir="ltr" style="margin: 12px 0px 0px; outline: none; posit
 ion: relative; color: #212121; font-size: 11pt; font-style: normal; font-we
 ight: 400; font-family: Lato, sans-serif; line-height: 1.6667; letter-spaci
 ng: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform
 : none; widows: 2; word-spacing: 0px; white-space: normal;"><span style="fo
 nt-family: Lato, Arial; font-variant: normal; font-weight: bold;">Title</sp
 an><span style="font-variant: normal;">:&nbsp;</span>The generalized Pitman
 -Stanley flow polytope</p><p dir="ltr" style="margin: 12px 0px 0px; outline
 : none; position: relative; color: #212121; font-size: 11pt; font-style: no
 rmal; font-weight: 400; font-family: Lato, sans-serif; line-height: 1.6667;
  letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; t
 ext-transform: none; widows: 2; word-spacing: 0px; white-space: normal;"><s
 pan style="font-family: Lato, Arial; font-variant: normal; font-weight: bol
 d;">Abstract</span><span style="font-variant: normal;">:&nbsp;</span>In 199
 9, Pitman and Stanley introduced the polytope bearing their name along with
  a study of its faces, lattice points, and volume. This polytope is well-st
 udied due to its connections to parking functions, lattice path matroids, g
 eneralized permutahedra/polymatroids, and flow polytopes. Its lattice point
 s correspond to plane partitions of skew shape with entries 0 and 1. Pitman
  and Stanley remarked that their polytope can be generalized so that lattic
 e points correspond to plane partitions of skew shape with entries 0,1,...,
 m. Since then, this generalization has been untouched. We study this polyto
 pe and 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 fo
 rmulas 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 Standa
 rd Young Tableaux. The new formulas come from the volume polynomial formula
 s of flow polytopes in terms of vector partition functions of Baldoni and V
 ergne and lattice point formulas of Stanley of marked order polytopes.</p><
 p dir="ltr" style="margin: 12px 0px 0px; outline: none; position: relative;
  color: #212121; font-size: 11pt; font-style: normal; font-weight: 400; fon
 t-family: Lato, sans-serif; line-height: 1.6667; padding-bottom: 0px; lette
 r-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-tr
 ansform: none; widows: 2; word-spacing: 0px; white-space: normal;">This is 
 joint work with Maura Hegarty, William Dugan, and Annie Raymond.</p>
CONTACT:Alejandro Morales 
DTSTAMP:20260830T041901
DTSTART;TZID=America/New_York:20250326T104500
DTEND;TZID=America/New_York:20250326T234500
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