Pith Number

pith:UAE3PPSM

pith:2026:UAE3PPSMUFCDHVBKHZSQAVPUEK

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New Bounds for Integer Flows and Verma Modules, via Denormalized Lorentzian Laurent Series

Jonathan Leake, Maryam Mohammadi Yekta

Denormalized Lorentzian Laurent series yield new bounds on integer flows in DAGs and on weight space dimensions in parabolic Verma modules.

arxiv:2605.15136 v1 · 2026-05-14 · math.CO

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Claims

C1strongest claim

We develop an analogous class of power series called denormalized Lorentzian (DL) Laurent series. This class is the natural generalization of DL polynomials to homogeneous power series with the benefit of capturing a number of combinatorial generating series including the Kostant partition function for integer flows of directed graphs. We then analyze specific DL Laurent series to obtain new bounds for integral flows on general directed acyclic graphs and new bounds for the dimensions of weight spaces of parabolic sl_{n+1}(C) Verma modules.

C2weakest assumption

That the Kostant partition function and the relevant generating series for parabolic Verma modules satisfy the defining properties of denormalized Lorentzian Laurent series, allowing the log-concavity or other inequalities to transfer and produce the stated bounds.

C3one line summary

Denormalized Lorentzian Laurent series are defined and used to prove new bounds for integral flows on DAGs and weight-space dimensions in parabolic sl_{n+1} Verma modules.

References

60 extracted · 60 resolved · 0 Pith anchors

[1] Br\"and\'en, Petter and Leake, Jonathan and Pak, Igor , TITLE =. Israel J. Math. , FJOURNAL =. 2023 , NUMBER =. doi:10.1007/s11856-022-2364-9 , URL = 2023 · doi:10.1007/s11856-022-2364-9

[2] Br\"and\'en, Petter and Huh, June , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2020 , NUMBER =. doi:10.4007/annals.2020.192.3.4 , URL = 2020 · doi:10.4007/annals.2020.192.3.4

[3] Anari, Nima and. Log-concave polynomials,. Duke Math. J. , FJOURNAL =. 2021 , NUMBER = 2021

[4] Advances in combinatorial mathematics , PAGES = 2009 · doi:10.1007/978-3-642-03562-3

[5] Narayanan, Hariharan , TITLE =. J. Algebraic Combin. , FJOURNAL =. 2006 , NUMBER =. doi:10.1007/s10801-006-0008-5 , URL = 2006 · doi:10.1007/s10801-006-0008-5

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Receipt and verification

First computed	2026-05-17T21:40:25.601336Z
Last reissued	2026-05-17T21:57:18.915607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

a009b7be4ca14433d42a3e650055f4229c0592269f0b7f0df1f6d5db6113138a

Aliases

arxiv: 2605.15136 · arxiv_version: 2605.15136v1 · pith_short_12: UAE3PPSMUFCD · pith_short_16: UAE3PPSMUFCDHVBK · pith_short_8: UAE3PPSM

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/UAE3PPSMUFCDHVBKHZSQAVPUEK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a009b7be4ca14433d42a3e650055f4229c0592269f0b7f0df1f6d5db6113138a

Canonical record JSON

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    "abstract_canon_sha256": "0630601dd3c983d4d70b62579f06a0a72468ac27b9d5b165fb902d81555fadf3",
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T17:42:37Z",
    "title_canon_sha256": "668de17ff79f718f52b3e4a0d81c8e926882b714413ba072a6154b31c056dc14"
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