Publications of Karola Mészáros

Research papers:

• M-convexity of Grothendieck polynomials via bubbling
  joint with Elena Hafner and Linus Setiabrata and Avery St. Dizier
  Submitted.
  
  
• Log-concavity of the Alexander polynomial
  joint with Elena Hafner and Alexander Vidinas
  Submitted.
  
  
• On the degree of Grothendieck polynomials
  joint with Matt Dreyer and Avery St. Dizier
  Submitted.
  
  
• On supports of Grothendieck polynomials
  joint with Linus Setiabrata and Avery St. Dizier
  Submitted.
  
  
• Principal specialization of dual characters of flagged Weyl modules
  joint with Avery St. Dizier and Arthur Tanjaya
  Electron. J. Combin. 28 (4) (2021), \#P4.17
  
  
• Inclusion-exclusion on Schubert polynomials
  joint with Arthur Tanjaya
  Algebr. Comb., accepted.
  
  
• An orthodontia formula for Grothendieck polynomials
  joint with Linus Setiabrata and Avery St. Dizier
  Trans. Amer. Math. Soc., 375 (2022), 1281-1303.
  
  
• Lorentzian polynomials from polytope projections
  joint with Linus Setiabrata
  Algebr. Comb., Volume 4 (2021) no. 4, pp. 723-739.
  
  
• Logarithmic concavity of Schur and related polynomials
  joint with June Huh, Jacob Matherne, and Avery St. Dizier
  Trans. Amer. Math. Soc. 375 (2022), no. 6, 4411--4427.
  
  Here is the code utilized in the paper.
  
  
• Counting integer points of flow polytopes
  joint with Kabir Kapoor and Linus Setiabrata
  Discrete Comput. Geom., accepted.
  
  
• Zero-one Schubert polynomials
  joint with Alex Fink and Avery St. Dizier
  Math. Z. 297 (2021), no. 3-4, 1023-1042.
  
  
• Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytope
  joint with Ricky I. Liu and Avery St. Dizier
  Combin. Theory, accepted.
  
  
• Gelfand-Tsetlin polytopes: a story of flow and order polytopes
  joint with Ricky I. Liu and Avery St. Dizier
  SIAM J. Disc. Math. 33 (2019), no. 4, 2394‐2415.
  
  
• Root cones and the resonance arrangement
  joint with Samuel C. Gutekunst and T. Kyle Petersen
  Electron. J. Combin. 28 (1) (2021), \#P1.12.
  
  
• Volumes and Ehrhart polynomials of flow polytopes
  joint with Alejandro H. Morales
  Math. Z. 293 (2019), no. 3-4, 1369‐1401. (journal link)
  
  
• Flow polytopes of partitions
  joint with Connor Simpson and Zoe Wellner,
  Electron. J. Combin. 26 (2019), no. 1, Paper 1.47, 12 pp. (journal link)
  
  
• Schubert polynomials as integer point transforms of generalized permutahedra
  joint with Alex Fink and Avery St. Dizier.
  Adv. Math. 332 (2018), 465‐475. (journal link)
  
  Here is the code utilized in the paper.
  
  
• From generalized permutahedra to Grothendieck polynomials via flow polytopes
  joint with Avery St. Dizier
  Algebr. Comb. 3 (2020), no. 5, 1197‐1230.
  
  Here is the code utilized in the paper.
  
  
  
• Volumes of generalized Chan-Robbins-Yuen polytopes
  joint with Sylvie Corteel and J. S. Kim.
  Discrete Comput. Geom. 65 (2021), no. 2, 510-530. (journal link)
  
  
• Flow polytopes with Catalan volumes
  joint with Sylvie Corteel and J. S. Kim.
  C. R. Acad. Sci. Paris, Ser. I, 355 (2017), no. 3, 248–259. (journal link)
  
  
• Flow polytopes and the space of diagonal harmonics
  joint with A.H. Morales and R. I. Liu.
  Canad. J. Math., 71 (2019), no. 6, 1495–1521. (journal link)
  
  
• On flow polytopes, order polytopes, and certain faces of the alternating sign matrix polytope
  joint with A.H. Morales and J. Striker
  Discrete Comput. Geom. 62 (2019), no. 1, 128–163. (journal link)
  
  
• Toric matrix Schubert varieties and their polytopes
  joint with L. Escobar
  Proc. Amer. Math. Soc. 144 (2016), no. 12, 5081–5096. (journal link)
  
  
• Calculating Greene's function via root polytopes and subdivision algebras
  Pacific J. Math. 286 (2017), no. 2, 385–400. (journal link)
  
  
• Subword complexes via triangulations of root polytopes
  joint with L. Escobar
  Algebr. Comb. 1 (2018), no. 3, 395–414. (journal link)
  
  
• Pipe dream complexes and triangulations of root polytopes belong together
  SIAM J. Discrete Math. 30 (2016), no. 1, 100–111. (journal link)
  
  
• The polytope of Tesler matrices
  joint with A.H. Morales and B. Rhoades.
  Selecta Math. 23 (2017), no. 1, 425–454. (journal link)
  
  Here is the code utilized in the paper.
  
  
• SB-labelings and posets with each interval homotopy equivalent to a sphere or a ball
  joint with P. Hersh.
  J. Combin. Theory Ser. A, (2017), 152, 104–120. (journal link)
  
  
• h-polynomials via reduced forms
  Electron. J. Combin. 22 (2015), no. 4, Paper 4.18, 17 pp. (journal link)
  
  
• h-polynomials of reduction trees
  SIAM J. Discrete Math. 30 (2016), no. 2, 736–762. (journal link)
  
  
• Subalgebras of the Fomin-Kirillov algebra
  joint with J. Blasiak and R. I. Liu.
  J. Algebraic Combin. 44 (2016), no. 3, 785–829. (journal link)
  
  
• How to decompose a permutation into a pair of labeled Dyck paths by playing a game
  joint with L. J. Billera and L. Levine.
  Proc. Amer. Math. Soc. 143 (2015), no. 5, 1865–1873. (journal link)
  
  
• Schur times Schubert via the Fomin-Kirillov algebra
  joint with G. Panova and A. Postnikov.
  Electron. J. Combin. 21(1) (2014), P1.39. (journal link)
  
  
• Flow polytopes of signed graphs and the Kostant partition function
  joint with A.H. Morales.
  Int. Math. Res. Notices (2015) no. 3: 830–871. (journal link)
  
  Here is the code utilized in the paper.
  
  
• Dyck tilings, linear extensions, descents, and inversions
  joint with J.S. Kim, G. Panova and D.B. Wilson.
  J. Combin. Theory Ser. A 122 (2014), 9–27. (journal link)
  
  
• Product formulas for volumes of flow polytopes
  Proc. Amer. Math. Soc. 143 (2015), no. 3, 937‐954. (journal link)
  
  
• Labeling the Regions of the Type C Shi Arrangement
  Electron. J. Combin. 20, Issue 2 (2013), P31. (journal link)
  
  
• Demystifying a divisibility property of the Kostant partition function
  Pacific J. Math. 260-1 (2012) 215–225. (journal link)
  
  
• Branched polymers and hyperplane arrangements
  joint with A. Postnikov
  Discrete Comput. Geom. 50, Issue 1 (2013), Page 22-38. (journal link)
  
  
• Root polytopes, triangulations, and the subdivision algebra, II,
  Trans. Amer. Math. Soc. 363 (2011) 6111–6141. (journal link)
  
  
• Root polytopes, triangulations, and the subdivision algebra, I ,
  Trans. Amer. Math. Soc. 363 (2011) 4359–4382. (journal link)
  
  
• Chip-firing and rotor-routing on directed graphs
  joint with A. Holroyd, L. Levine, Y. Peres, J. Propp, and D. Wilson.
  In and out of Equilibrium II, "Progress in Probability,'' Birkhauser (2008), 331–364. (book chapter link)
  
  
• On the number of genus one labeled circle trees
  Electron. J. Combin. 14 (2007), #R68. (journal link)
  
  
• Generalized Latin squares and their defining sets
  Discrete Math. 308, Issue 12 (2008), 2366–2378. (journal link)
  
  
• On low degree k-ordered graphs
  Discrete Math. 308, Issue 12 (2008), 2418–2426. (journal link)
  
  
• On 3-regular 4-ordered graphs
  Discrete Math. 308, Issue 11 (2008), 2149–2155. (journal link)

Thesis:

• Root polytopes, triangulations, and subdivision algebras
  Ph.D. Thesis advised by Richard P. Stanley, MIT (2010)