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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:<div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focus
 out:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" 
 style="display: inline-block; max-width: 100%; position: relative;"><span s
 tyle="font-family: Lato, Arial; font-size: 11pt; 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: baseline;">26</span><span style="fo
 nt-size: 11pt; font-variant: normal; vertical-align: baseline;">/2025</span
 ></div><p dir="ltr" style="margin: 12px 0px 0px; outline: none; position: r
 elative; color: #212121; font-size: 11pt; font-style: normal; font-weight: 
 400; font-family: Lato, sans-serif; line-height: 1.6667; letter-spacing: no
 rmal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none
 ; widows: 2; word-spacing: 0px; white-space: normal;"><span style="font-fam
 ily: Lato, Arial; font-variant: normal; font-weight: bold;">Speaker</span><
 span style="font-variant: normal;">:&nbsp;</span><a href="https://sites.goo
 gle.com/view/ahmorales/" target="_blank" rel="noopener" style="color: inher
 it; text-decoration: none;"><span style="color: #006580; text-decoration: u
 nderline;">Alejandro Morales</span></a>&nbsp;(Montreal)</p><p dir="ltr" sty
 le="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: none; widows: 2; word-spaci
 ng: 0px; white-space: normal;"><span style="font-family: Lato, Arial; font-
 variant: normal; font-weight: bold;">Title</span><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; c
 olor: #212121; font-size: 11pt; font-style: normal; font-weight: 400; font-
 family: Lato, sans-serif; line-height: 1.6667; letter-spacing: normal; orph
 ans: 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 styl
 e="font-variant: normal;">:&nbsp;</span>In 1999, Pitman and Stanley introdu
 ced the polytope bearing their name along with a study of its faces, lattic
 e points, and volume. This polytope is well-studied due to its connections 
 to parking functions, lattice path matroids, generalized permutahedra/polym
 atroids, and flow polytopes. Its lattice points correspond to plane partiti
 ons of skew shape with entries 0 and 1. Pitman and Stanley remarked that th
 eir polytope can be generalized so that lattice points correspond to plane 
 partitions of skew shape with entries 0,1,...,m. Since then, this generaliz
 ation has been untouched. We study this polytope 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 formulas for the number of vert
 ices and faces as well as old and new formulas for the number of lattice po
 ints and volume in terms of rectangular Standard Young Tableaux. The new fo
 rmulas come from the volume polynomial formulas of flow polytopes in terms 
 of vector partition functions of Baldoni and Vergne and lattice point formu
 las of Stanley of marked order polytopes.</p><p dir="ltr" style="margin: 12
 px 0px 0px; outline: none; position: relative; color: #212121; font-size: 1
 1pt; font-style: normal; font-weight: 400; font-family: Lato, sans-serif; l
 ine-height: 1.6667; padding-bottom: 0px; letter-spacing: normal; orphans: 2
 ; text-align: start; text-indent: 0px; text-transform: none; widows: 2; wor
 d-spacing: 0px; white-space: normal;">This is joint work with Maura Hegarty
 , William Dugan, and Annie Raymond.</p>
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:20260829T213128
DTSTART;TZID=America/New_York:20250326T104500
DTEND;TZID=America/New_York:20250326T234500
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
END:VCALENDAR